Integrated circuit for transmission apparatus

ABSTRACT

Disclosed are an encoder, a transmission device, and an encoding method with which the transmission amount is reduced and a deterioration in transmission efficiency is suppressed while improving reception quality when QC-LDPC or a like block encoding is used. A puncture pattern setting unit ( 620 ) searches for a puncture pattern for each integral multiple of the number of columns or for each divisor of the number of columns of a sub block matrix that forms a check matrix (H) of a QC-LDPC code, and a puncture unit (data reduction unit) ( 630 ) switches the puncture pattern for each integral multiple of the number of columns or for each divisor of the number of columns of the sub block matrix that forms the check matrix of the QC-LDPC code.

TECHNICAL FIELD

The present invention relates to an encoder, a transmitting apparatusand a coding method that form a coded sequence using a parity generatormatrix that partially or regularly includes zero matrixes such asQC-LDPC (Quasi Cyclic Low Density Parity Check) code.

BACKGROUND ART

In recent years, low density parity check (LDPC: Low Density ParityCheck) code is becoming popular as error correction code that makes themost of high error correction performance on a feasible circuit scale.The LDPC code is an error correction code defined by a low densityparity check matrix H. “Low density” means that the number of “1”elements included in a matrix is considerably smaller than the number of“0” elements. The LDPC code is a block code having the same block lengthas the number of columns N of parity check matrix H.

Because of its high level error correction performance and ease ofmounting, the LDPC code is adopted for a high-speed wireless LAN (LocalArea Network) system of IEEE802.11n and an error correction codingscheme such as a digital broadcasting system. Furthermore, an adoptionof QC (Quasi Cyclic)-LDPC code on a home network is also under study.

The block code has a feature that the error correction performanceimproves as the block code length increases. When, for example, symbolssuch as a header for transmitting control information or the like arewished to be transmitted reliably, receiving quality of the header canbe secured using a block code longer than the header.

Furthermore, using the same error correction code as the errorcorrection code used to transmit information and the error correctioncode used to transmit the header is advantageous from the perspective ofthe circuit scale. The present application refers to and describes asymbol for transmitting control information or the like as “header,” buta symbol for transmitting control information or the like may also bereferred to as “control symbol (control channel or control signal),”“preamble,” “tail symbol,” “pilot symbol (pilot channel or pilotsignal),” “training symbol” or the like.

In this case, as shown in FIG. 1, when the number of information bitsthat need to be transmitted (e.g., header length) is less than the blocklength of the block code, parity bits are generated by performing codingassuming that information bits in the excess part of the block lengthare 0's.

As a coded sequence to be actually transmitted, only information bitsthat need to be transmitted (e.g., header) and parity bits aretransmitted as shown, for example, in FIG. 1. That is, the portion ofinformation bits assumed to be 0's is not actually transmitted.

A header of control information, for example, generally has a smallernumber of bits than payload data that transmits information such as animage. However, by transmitting the header and parity bits as shown inFIG. 1, the header and payload data can be encoded using the same blockcode. Furthermore, since the header is encoded using the block code of agreater block length than the header length, receiving quality of theheader can be secured. As a result, since the header can be reliablytransmitted to the communicating party, the aforementioned communicationmethod is effective in establishing communication.

CITATION LIST Non-Patent Literature

NPL 1

-   “Rate Estimation Techniques for Rate-Compatible LDPC Codes,” IEICE    (Institute of Electronics, Information and Communication Engineers)    transactions 2006/12 Vol. J89 A N0.12 p. 1177    NPL 2-   M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes    from circulant permutation matrices,” IEEE Trans. Inform. Theory,    vol. 50, no. 8, pp. 1788-1793, November 2001.    NPL 3-   L. Chen, J. Xu, I. Djurdjevic, and S. Lin, “Near-Shannon limit    quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun.,    vol. 52, no. 7, pp. 1038-1042, July 2004.    NPL 4-   IEEE Unapproved Draft Std P802.11n_D3.00, pp. 274, September 2007    NPL 5-   D. J. C. Mackay, “Good error-correcting codes based on very sparse    matrices,” IEEE Trans. Inform. Theory, vol. 45, no. 2, pp 399-431,    March 1999.    NPL 6-   M. P. C. Fossorier, M. Mihaljevic, and H. Imai, “Reduced complexity    iterative decoding of low density parity check codes based on belief    propagation,” IEEE Trans. Commun., vol. 47, no. 5, pp. 673-680, May    1999.    NPL 7-   J. Chen, A. Dholakia, E. Eleftheriou, M. P. C. Fossorier, and X.-Yu    Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans.    Commun., vol. 53., no. 8, pp. 1288-1299, August 2005.

SUMMARY OF INVENTION Technical Problem

However, when data such as a header having a smaller data length thanthe block length is encoded, the prior arts can improve receivingquality, but also have to transmit parity bits obtained through codingassuming that information bits are 0's. Thus, when the header length isequivalent to the block length and its length is short, the number ofparity bits that need to be transmitted is small. On the contrary, whenthe block length is greater than the header length, the number of paritybits that need to be transmitted increases, and the prior arts have aproblem that data transmission efficiency deteriorates. Therefore,solving the problem of deterioration of data transmission efficiencywill provide an advantage of being able to improve data transmissionefficiency as well as receiving quality.

It is therefore an object of the present invention to provide anencoder, a transmitting apparatus and a coding method capable ofreducing, when using a block code such as QC-LDPC code, the amount oftransmission and suppressing deterioration of transmission efficiencywhile improving receiving quality.

Solution to Problem

An encoder of the present invention includes: a coding section thatgenerates coded sequence s that satisfies equation (14-1), equation(14-2) and equation (14-3) for information bit sequence u; and a settingsection that sets a y-th puncturing pattern which corresponds to thenumber of columns z ranging from zxy+1 columns (y is an integer between0 and (n_(b)−1)) to z×(y+1) columns, and which has a cycle of divisorsof the number of columns z, and, with this encoder, in the codedsequence s made up of z×n_(b) bits from a first bit to a z×n_(b)-th bit,bits to be removed are determined from a z×y+1-th bit to a z×(y+1)-thbit, based on the y-th puncturing pattern, the bits determined to beremoved are removed from the z×n_(b) bits making up the coded sequence sto form a transmission information bit sequence, and the transmissioninformation bit sequence is outputted.

A transmitting apparatus of the present invention adopts a configurationincluding a transmission section that is provided with the abovedescribed encoder and transmits the transmission information bitsequence.

A coding method of the present invention includes the steps of:generating coded sequence s that satisfies equation (16-1), equation(16-2) and equation (16-3) for information bit sequence u; and setting ay-th puncturing pattern which corresponds to the number of columns zranging from z×y+1 columns (y is an integer between 0 and (n_(b)−1)) toz×(y+1) columns, and which has a cycle of divisors of the number ofcolumns z, and, with this coding method, in the coded sequence s made upof z×n_(b) bits from a first bit to a z×n_(b)-th bit, bits to be removedare determined from a z×y+1-th bit to a z×(y+1)-th bit, based on they-th puncturing pattern, the bits determined to be removed are removedfrom the z×n_(b) bits making up the coded sequence s to form atransmission information bit sequence and the transmission informationbit sequence is outputted.

Advantageous Effects of Invention

According to the communication apparatus and the communication method ofthe present invention, when using a block code such as QC-LDPC code, itis possible to reduce the amount of transmission and suppressdeterioration of transmission efficiency while improving receivingquality.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram illustrating a block configuration example of blockcode and a coded sequence that is actually transmitted;

FIG. 2 is a diagram illustrating input and output data of an encoderused for a communication apparatus according to Embodiment 1 of thepresent invention;

FIG. 3 is a diagram illustrating an example of parity generator matrix gof QC-LDPC code;

FIG. 4 is a diagram illustrating an example of zero matrix;

FIG. 5 is a diagram illustrating another example of zero matrix;

FIG. 6 is a diagram illustrating a configuration example of the encoderaccording to Embodiment 1;

FIG. 7 is a diagram illustrating a configuration example of a decoderaccording to Embodiment 1;

FIG. 8 is a diagram illustrating a frame configuration example of amodulated signal transmitted by communication apparatus #1;

FIG. 9 is a diagram illustrating a configuration example ofcommunication apparatus #1 having the encoder according to Embodiment 1;

FIG. 10 is a diagram illustrating a configuration example ofcommunication apparatus #2 having the decoder according to Embodiment 1;

FIG. 11 is a diagram illustrating a configuration example of one blockof QC-LDPC code;

FIG. 12 is a diagram illustrating a configuration example of an encoderaccording to Embodiment 2 of the present invention;

FIG. 13 is a diagram illustrating an example of arrangement ofinformation bits;

FIG. 14 is a diagram illustrating the correspondence between data lengthα and a method of reducing parity bits to be transmitted;

FIG. 15 is a diagram illustrating a configuration example of an encoderaccording to Embodiment 3 of the present invention;

FIG. 16A is a diagram illustrating a method of switching betweenpuncturing patterns;

FIG. 16B is another diagram illustrating a method of switching betweenpuncturing patterns;

FIG. 16C is a further diagram illustrating a method of switching betweenpuncturing patterns;

FIG. 17 is a diagram illustrating an example of arrangement of controlinformation;

FIG. 18 is a diagram illustrating an example of arrangement of controlinformation according to Embodiment 4 of the present invention;

FIG. 19A is a diagram illustrating an application example of puncturingpattern according to Embodiment 5 of the present invention;

FIG. 19B is a diagram illustrating another application example ofpuncturing pattern according to Embodiment 5;

FIG. 19C is a diagram illustrating a further application example ofpuncturing pattern according to Embodiment 5;

FIG. 20A is a diagram illustrating a still further application exampleof puncturing pattern according to Embodiment 5;

FIG. 20B is a diagram illustrating a still further application exampleof puncturing pattern according to Embodiment 5;

FIG. 20C is a diagram illustrating a still further application exampleof puncturing pattern according to Embodiment 5;

FIG. 21 is a diagram illustrating an application example of puncturingpattern according to Embodiment 6 of the present invention;

FIG. 22 is a diagram illustrating another application example ofpuncturing pattern according to Embodiment 6;

FIG. 23 is a diagram illustrating a puncturing pattern according toEmbodiment 7 of the present invention;

FIG. 24 is a diagram illustrating parity check matrix H_(b) of QC-LDPCcode having coding rate 5/6;

FIG. 25 is a diagram illustrating an example of puncturing patternaccording to Embodiment 7;

FIG. 26 is a diagram illustrating another example of puncturing patternaccording to Embodiment 7; and

FIG. 27 is a diagram illustrating an example of parity check matrixH_(b) of QC-LDPC code having coding rate 1/2 and puncturing pattern.

DESCRIPTION OF EMBODIMENTS

Hereinafter, embodiments of the present invention will be described indetail with reference to the accompanying drawings.

Embodiment 1

FIG. 2 illustrates input and output data of an encoder used for acommunication apparatus of the present invention. Encoder 100 in FIG. 2forms a QC-LDPC (Quasi Cyclic Low Density Parity Check) code.

In FIG. 2, information sequence u=(x1, x2, . . . , xm) is input data ofencoder 100 and coded sequence s=(x1, x2, . . . , xm, p1, p2, . . . ,pn) represents output data of the encoder.

Equation 1 represents parity check matrix H of the QC-LDPC code (seeNon-Patent Literature 1, Non-Patent Literature 2 and Non-PatentLiterature 3).

$\begin{matrix}\lbrack 1\rbrack & \; \\{H = \begin{bmatrix}{I\left( p_{0,0} \right)} & {I\left( p_{0,1} \right)} & \ldots & {I\left( p_{0,{L - 1}} \right)} \\{I\left( p_{1,0} \right)} & {I\left( p_{1,1} \right)} & \ldots & {I\left( p_{1,{L - 1}} \right)} \\\vdots & \vdots & \ddots & \vdots \\{I\left( p_{{J - 1},0} \right)} & {I\left( p_{{J - 1},1} \right)} & \ldots & {I\left( p_{{J - 1},{L - 1}} \right)}\end{bmatrix}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

In equation 1, 0≤j≤J−1, 0≤1≤L−1 and parity check matrix H has codelength N=p×L (p is a natural number). Furthermore, subblock matrixI(p_(j,1)) is a cyclic permutation matrix of q rows and r columnswhere(r=(q+p_(j,1)) mod p(0≤q≤p−1)) is 1 and “0” otherwise. p_(j,1) isdetermined to be “0” or “1” by randoms.

Encoder 100 in FIG. 2 generates a coded sequence using generator matrixG. Here, generator matrix G has the relationship of equation 2 withparity check matrix H.

[2]GH ^(T)=0  (Equation 2)

Coded sequence s can be represented as s^(T)=Gu^(T) using informationsequence u and generator matrix G. Since the QC-LDPC code is asystematic code, generator matrix G can be expressed as shown inequation 3.

$\begin{matrix}\lbrack 3\rbrack & \; \\{G = \begin{bmatrix}I \\g\end{bmatrix}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

Here, I is a unit matrix of m×m. Furthermore, when only parity sequencew is extracted from coded sequence s and defined as w=(p1, p2, . . . ,pn), matrix g is a matrix (parity generator matrix) to obtain paritysequence w. Parity generator sequence w satisfies w^(T)=gu^(T).

FIG. 3 illustrates an example of parity generator matrix g of theQC-LDPC code. The QC-LDPC code illustrated in FIG. 3 is a QC-LDPC codehaving a coding rate (R)=1/2, LDPC code information block length(bits)=648, LDPC codeword block length (bits)=1296 described in Table20-14 (LDPC parameters) of Non-Patent Literature 4.

Parity generator matrix g illustrated in FIG. 3 is made up of aplurality of subblock matrixes 201, 202, . . . , 211, 212, . . . . Forexample, in subblock matrix 201 in FIG. 3, each (i+1)-th row elementassumes a value shifting each i-th row element (i is a natural number)one bit (one column) to the right. Likewise, in subblock matrix 211 inFIG. 3, each (i+1)-th row element assumes a value shifting each i-th rowelement (i is a natural number) one bit to the right.

Furthermore, in subblock matrix 202 in FIG. 3, each second row elementassumes a value shifting each first row element one bit to the right.Likewise, in subblock matrix 212 in FIG. 3, each second row elementassumes a value shifting each first row element one bit to the right.

Thus, subblock matrixes 201, 202, . . . , 211, 212 can be said to becyclic permutation matrixes. In the example shown in FIG. 3, subblockmatrixes 201, 202, . . . , 211, 212 are matrixes of 27 rows and 27columns.

Furthermore, in parity generator matrix g, subblock matrixes of the samecolumn are related to each other. For example, when subblock matrix 201is compared with subblock matrix 211 of the same column as that ofsubblock matrix 201, the i-th row element of subblock matrix 211 isdifferent from the (i+1)-th row element (i is a natural number) ofsubblock matrix 201 only in the second bit.

Likewise, when subblock matrix 202 is compared with subblock matrix 212of the same column as that of subblock matrix 202, the i-th row elementof subblock matrix 212 is the same as the (i+1)-th row element (i is anatural number) of subblock matrix 201.

In a vertical view of the subblock matrix of 27 rows and 27 columns, forexample, in a vertical view of subblock matrix 201 and subblock matrix211, as described above, although these subblock matrixes are related toeach other, the subblock matrixes are not always identical matrixes.

Furthermore, a feature of parity generator matrix g is that 0 elementsare arranged consecutively. Thus, as is clear from FIG. 4 illustratingparity generator matrix g identical to that in FIG. 3, it is possible tosecure matrix 221 in which the elements to constitute the matrix are all0's in subblock matrix 202. Hereinafter, a matrix in which the elementsto constitute the matrix are all 0's will be referred to as “zeromatrix.”

Furthermore, it is possible to secure zero matrix 222 which starts fromthe same column as that of zero matrix 221 and in which the number ofcolumns is the same magnitude as zero matrix 221 in subblock matrix 212.In parity generator matrix g, there are many zero matrixes which startfrom the same column as that of zero matrix 221 and in which the numberof columns is the same magnitude as in zero matrix 221.

Thus, the parity generator matrix of QC-LDPC code includes zero matrixesand has a feature that there are many zero matrixes which start from thesame column of the parity generator matrix.

The present inventors have focused on this feature of parity generatormatrix g of QC-LDPC code. That is, the present inventors have focused onthe fact that when 0's are arranged in columns other than those of zeromatrixes of m rows and n columns as information bits, all the m paritybits generated become 0's. Furthermore, the present inventors havefocused on the fact that subblock matrixes having the same column arerelated to each other in the arrangement of elements in parity generatormatrix g, and there are many zero matrixes which start from the samecolumn in parity generator matrix g of QC-LDPC code, and therefore byarranging 0's in columns other than those of zero matrixes asinformation bits, many parity bits which become all 0's are generated.

That is, when the number of information bits that need to be transmittedis less than the block length of the block code and coding is performedassuming that some information bits are 0's, if the information bitsthat need to be transmitted are arranged in the column of zero matrixes(m rows and n columns) and 0's are arranged outside the zero matrixes (mrows and n columns) as imaginary bits, m parity bits having “0” valuesare generated. These parity bits are always 0's regardless of theinformation bits that need to be transmitted.

Therefore, since the receiving side knows the positions of m parity bitsalways having “0” values from the positions of the zero matrixes, thereceiving side can decode all data even if the transmitting side doesnot transmit m parity bits always having “0” values. Furthermore, thereceiving side can set m parity bits always having “0” values as bitsnot to transmit by the transmitting apparatus, that is, such bits can bereduced as redundant bits.

This will be described in further detail using FIG. 4 again. Attentionwill be focused on zero matrix 221 in FIG. 4. Zero matrix 221 in FIG. 4is a matrix of 7 rows and 12 columns and information bits correspondingto the columns of zero matrix 221 are x36 to x47. Thus, when coding isperformed with information bits that need to be transmitted arranged inx36 to x47 and information bits “0” arranged in other than x36 to x47,p1 to p7 are always 0's regardless of the values of x36 to x47.

Likewise, focusing on zero matrix 222 whose column positions in paritygenerator matrix g are the same as those of zero matrix 221, if codingis performed with information bits “0” arranged in other than x36 tox47, p28 to p34 are always 0's regardless of the values of x36 to x47.

Therefore, of parity bits p1 to p54 generated by parity generator matrixg, p1 to p7 and p28 to p34 always have “0” values. Thus, when thetransmitting apparatus does not transmit parity bits p1 to p54 alwayshaving “0” values generated by parity generator matrix g, bits to betransmitted by the transmitting apparatus can be reduced to only x36 tox47 and p8 to p27, p35 to p54. Although a case has been described abovefocusing on p1 to p54 as an example, it is possible to reduce the numberof parity bits to be transmitted by the transmitting apparatus from p55onward as well.

Since zero matrix 221 in FIG. 4 has 7 rows and 12 columns, wheninformation bits that need to be transmitted are 12 bits or less,information bits that need to be transmitted may be arranged in columnsof zero matrix 221.

When information bits that need to be transmitted exceed 12 bits,information bits that need to be transmitted may be further arranged incolumns of zero matrixes 231 and 232 as shown, for example, in FIG. 5.As a feature of a parity generator matrix of QC-LDPC code, since 0's arearranged consecutively, there are many zero matrixes such as zeromatrixes 231 and 232 in parity generator matrix g in addition to zeromatrixes 221, 222, . . . , as shown in FIG. 5.

Zero matrixes 231 and 232 are matrixes of 7 rows and 7 columns and evenwhen information bits that need to be transmitted are arranged in x71 tox77, p1 to p7 and p28 to p34 are all 0's. Therefore, the transmittingapparatus need not transmit p1 to p7 and p28 to p34 in the same way aswhen zero matrixes 221 and 222 are used.

Therefore, when zero matrixes 231 and 232 are used in addition to zeromatrixes 221 and 222, the information bits that need to be transmittedmay be arranged in x36 to x47 and x71 to x77. By this means, the maximumnumber of bits becomes 19 (=12+7) bits, and, compared to the case whereonly zero matrixes 221 and 222 are used, it is possible to increase themaximum number of bits that can be arranged as information bits thatneed to be transmitted.

Likewise, when the number of information bits that need to betransmitted exceeds 19 bits, zero matrixes included in other partialmatrixes may be used. FIG. 5 illustrates part of parity generator matrixg of QC-LDPC code, and there are 24 (=648/27) cyclic permutationmatrixes of 27 rows and 27 columns in parity generator matrix g ofQC-LDPC in the column direction, and therefore many zero matrixes arealso included in areas not shown. For this reason, the transmittingapparatus can increase the maximum number of bits that can be arrangedas information bits that need to be transmitted in the portions of zeromatrixes using zero matrixes in the same way as that described above.

Thus, focusing on the fact that there are a plurality of zero matrixesthat start from the same column of parity generator matrix g and thathave the same number of columns in parity generator matrix g of QC-LDPCcode, the present embodiment arranges information bits that need to betransmitted in columns of the zero matrixes and arranges 0's in columnsother than the zero matrixes as imaginary bits. Thus, parity bits havingthe same number of “0” values as the number of rows of the zero matrixesare generated.

In this case, if the transmitting apparatus and receiving apparatusshare the positions of zero matrixes with respect to parity generatormatrix g, even if parity bits corresponding to the rows of the zeromatrixes are not actually transmitted, the receiving side performsdecoding processing assuming that 0's have been transmitted, and canthereby decode coded data encoded by parity generator matrix g. Thus,the transmitting apparatus can reduce the number of parity bits thatneed to be transmitted and improve transmission efficiency.

A zero matrix may also have 1 row and 1 column. That is, when there area plurality of zero matrixes of 1 row and 1 column in the same row andthere is a row having “0” elements in the same column as in theplurality of zero matrixes, the same number of parity bits always having“0” as rows having “0” elements in the same column are generated.

That is, when the transmitting apparatus inserts 0's in information bitsand generates parity bits using information bits and 0's and matrixcalculation with the parity generator matrix of QC-LDPC code, thetransmitting apparatus removes parity bits always having “0” values ofthe parity bits based on the positions in which information bits arearranged and the parity generator matrix, outputs a parity sequenceafter the removal, transmits the parity sequence after the removal, andcan thereby reduce the number of parity bits that need to be transmittedand improve transmission efficiency.

Of the zero matrixes (including zero matrixes of 1 row and 1 column)that start from the same column of parity generator matrix g and thathave the same number of columns, the transmitting apparatus assumes amatrix having a maximum number of rows to be the zero matrix to be setarranges 0's outside columns of the set zero matrix so as to generatethe same number of parity bits having “0” values as rows of the set zeromatrix.

Therefore, the transmitting apparatus punctures the parity bits having“0” values as bits not to transmit, and can thereby improve transmissionefficiency. In this case, of the zero matrixes that start from the samecolumn of parity generator matrix g and that have the same number ofcolumns, the transmitting apparatus sets partial matrixes that areincluded more in parity generator matrix g as the zero matrixes, and canthereby reduce more parity bits.

In this case, the transmitting apparatus assumes the maximum number ofbits that can be arranged as information bits that need to betransmitted to be the number of columns of the zero matrixes. Forexample, for the transmitting apparatus, when zero matrix 221, 222, . .. are set as zero matrixes, the maximum number of bits in whichinformation bits that need to be transmitted can be arranged is 12 bits.

Furthermore, for the transmitting apparatus, when zero matrixes 231 and232 are set in addition to zero matrixes 221 and 222 as zero matrixes,the maximum number of bits in which information bits that need to betransmitted can be arranged is 19 bits. Conversely, the transmittingapparatus needs only to set zero matrixes according to the data length(number of bits) of information bits that need to be transmitted. Asdescribed above, a zero matrix may have 1 row and 1 column and may notnecessarily be consecutive.

FIG. 6 illustrates a configuration example of the encoder that performscoding using above described parity generator matrix g. Encoder 100 inFIG. 6 includes zero matrix setting section 110, arrangement section120, coding section 130 and puncturing section (data reducing section)140. Hereinafter, a case will be described where an information sequencehaving a fixed data length such as header is inputted to encoder 100 asan example.

Zero matrix setting section 110 sets a zero matrix which is a partialmatrix of parity generator matrix g of QC-LDPC in which all constituentelements are 0's. As for the method of setting a zero matrix, when thedata length of an information sequence is uniquely defined like aheader, a zero matrix having a number of columns equal to or more thanthe header length is set. Hereinafter, a case will be described wherezero matrixes 221, 222, . . . , in FIG. 4 are set as zero matrixes as anexample. Zero matrix setting section 110 outputs information about thepositions of zero matrixes in parity generator matrix g to arrangementsection 120 and puncturing section (data reducing section) 140.

Arrangement section 120 receives an information sequence such as aheader as input, arranges information bits (input bits) in columns ofzero matrixes based on information about the positions of zero matrixesreported from zero matrix setting section 110 and arranges 0's incolumns outside zero matrixes as imaginary bits.

When, for example, the positions of zero matrixes 221 and 222 arereported from zero matrix setting section 110, arrangement section 120arranges information bits (input bits) in columns x36 to x47 of zeromatrix 221 and arranges 0's outside x36 to x47. Arrangement section 120outputs the arranged bits to coding section 130.

Coding section 130 codes the bits outputted from arrangement section 120using parity generator matrix g and acquires coded sequence (informationbits and parity bits). Coding section 130 outputs the coded sequence topuncturing section (data reducing section) 140.

Puncturing section (data reducing section) 140 punctures (removes) 0'sarranged outside x36 to x47 from the coded sequence as bits not totransmit, based on the information about the positions of zero matrixes221 and 222 reported from zero matrix setting section 110.

Furthermore, puncturing section (data reducing section) 140 punctures(removes) parity bits p1 to p7, p28 to p34, . . . corresponding to rowsof zero matrixes 221 and 222 as bits not to transmit from the codedsequence based on the information about the positions of zero matrixes221 and 222 reported from zero matrix setting section 110.

Puncturing section (data reducing section) 140 outputs the codedsequence other than the punctured (reduced) bits as bits not to transmitfrom the coded sequence, as bits that need to be transmitted.

FIG. 7 illustrates a configuration example of a decoder that decodes asignal transmitted from the above described encoder.

Decoder 300 includes fixed log likelihood ratio insertion section 310and BP (Belief Propagation) decoding section 320.

Fixed log likelihood ratio insertion section 310 receives a received loglikelihood ratio calculated by a log likelihood ratio calculationsection (not shown) and a control signal indicating information aboutthe positions of zero matrixes as input and inserts a known loglikelihood ratio in the received log likelihood ratio according to thepositions of zero matrixes.

When, for example, zero matrixes 221 and 222, . . . , are used on thecoding side, received log likelihood ratios LLR_(x36) to LLR_(x47),LLR_(p8) to LLR_(p27), LLR_(p35) and onward corresponding to x36 to x47and p8 to p27, p35 and onward are inputted to fixed log likelihood ratioinsertion section 310. Thus, fixed log likelihood ratio insertionsection 310 inserts received log likelihood ratios LLR_(x1) toLLR_(x35), LLR_(x48) . . . , LLR_(p1) to LLR_(p7), LLR_(p28) toLLR_(p34) corresponding to x1 to x35, x48, . . . .

To be more specific, when zero matrixes 221 and 222, . . . are used onthe coding side, since this corresponds to 0's being transmitted as x1to x35, x48, . . . , p1 to p7, p28 to p34, . . . , fixed log likelihoodratio insertion section 310 inserts fixed log likelihood ratioscorresponding to known bits “0” as log likelihood ratios LLR_(x)1 toLLR_(x35), LLR_(x48) . . . , LLR_(p1) to LLR_(p7), LLR_(p28) toLLR_(p34) . . . of x1 to x35, x48 . . . . In FIG. 7, the received loglikelihood ratios encircled by broken line circles represent thereceived log likelihood ratios inserted by fixed log likelihood ratioinsertion section 310.

Fixed log likelihood ratio insertion section 310 outputs the insertedlog likelihood ratios to BP decoding section 320.

BP decoding section 320 performs decoding using, for example,sum-product decoding, min-sum decoding, Normalized BP decoding andoffset BP decoding described in Non-Patent Literature 5 to Non-PatentLiterature 7.

Hereinafter, the configuration of communication apparatus #1 having theencoder configured as described above and the configuration ofcommunication apparatus #2 that has the decoder configured as describedabove and receives a signal transmitted from communication apparatus #1will be described.

FIG. 8 illustrates a frame configuration example of a modulated signaltransmitted by communication apparatus #1. A control information symbolis a symbol for transmitting control information about a modulationscheme, error correction code used, coding rate, transmission method,data length or the like to the communicating party (communicationapparatus #2). An information symbol is a symbol for transmittinginformation bits and parity bits obtained through QC-LDPC coding.

FIG. 9 illustrates a configuration example of communication apparatus#1. In communication apparatus 400 in FIG. 9, coding section 410receives an information sequence as input and outputs a coded sequenceto interleaver 420. Coding section 410 is made up of encoder 100 in FIG.6.

Interleaver 420 receives the coded sequence as input, performsinterleaving and thereby obtains interleaved data. Interleaver 420 maynot always be provided depending on the type of code.

Mapping section 430 receives the interleaved data as input, performsmodulation such as QPSK (Quadrature Phase Shift Keying), 16QAM(Quadrature Amplitude Modulation) and thereby obtains a baseband signal.

Transmitting section 440 receives the baseband signal as input, appliespredetermined signal processing such as quadrature modulation, frequencyconversion, thereby obtains a modulated signal and transmits themodulated signal.

FIG. 10 illustrates a configuration example of communication apparatus#2. In communication apparatus 500 in FIG. 10, receiving section 510receives a received signal as input, applies predetermined radioprocessing such as frequency conversion and thereby obtains a basebandsignal. Receiving section 510 outputs the baseband signal to controlinformation detection section 520 and log likelihood ratio calculationsection 530.

Control information detection section 520 detects information about zeromatrixes, information about interleaving patterns and information aboutthe coding rate or the like from the baseband signal. Controlinformation detection section 520 then outputs the information about theinterleaving pattern to deinterleaver 540 and outputs the informationabout zero matrixes and information about the coding rate to decodingsection 550.

Log likelihood ratio calculation section 530 receives the basebandsignal as input, calculates a log likelihood ratio using, for example,the method shown in Non-Patent Literature 5 and obtains a log likelihoodratio per bit. Log likelihood ratio calculation section 530 outputs thelog likelihood ratio per bit to deinterleaver 540.

Deinterleaver 540 receives the log likelihood ratio per bit as input,applies corresponding processing of deinterleaving to interleaver 420and thereby obtains deinterleaved log likelihood ratios. When performingBP decoding, even when deinterleaver 540 is not provided, decodingsection 550 can perform decoding by providing a parity check matrix withdeinterleaving taken into account.

Decoding section 550 is made up of decoder 300 in FIG. 7. Decodingsection 550 receives the deinterleaved log likelihood ratios as input,performs decoding corresponding to coding section 410 and therebyobtains received data.

As described above, in the present embodiment, zero matrix settingsection 110 sets zero matrixes which are partial matrixes of paritygenerator matrix g and in which all elements are 0's. Arrangementsection 120 arranges input bits in columns of zero matrixes and arranges0's in columns outside the zero matrixes. Coding section 130 acquiresparity bits through coding using parity generator matrix g. Puncturingsection (data reducing section) 140 punctures (removes) 0's arranged incolumns outside zero matrixes as bits not to transmit, based oninformation about the positions of zero matrixes reported from zeromatrix setting section 110, and further punctures (removes) parity bitscorresponding to rows of zero matrixes of the parity bits obtained asbits not to transmit.

Thus, when inputting information bits and generating parity bits throughmatrix calculation between the information bits and a parity generatormatrix, encoder 100 arranges the information bits at positionscorresponding to columns of partial matrixes in which all elements are0's of the parity generator matrix, arranges 0's at positionscorresponding to columns outside the partial matrixes in which allelements are 0's and performs matrix calculation between the arrangedinformation bits, 0's and the parity generator matrix. Thus, encoder 100generates a parity sequence, removes parity bits always having “0”values of the parity sequence and outputs the parity sequence after theremoval.

In other words, encoder 100 inserts 0's in information bits, generatesparity bits through matrix calculation between the information bits, 0'sand the parity generator matrix of QC-LDPC code, removes parity bitsalways having “0” values of the parity bits based on the positions inwhich 0's are inserted and the parity generator matrix and outputs theparity sequence after the removal.

Therefore, in transmitting apparatus 400 having encoder 100,transmitting section 440 transmits input bits and parity bits other thanthe parity bits corresponding to rows of zero matrixes, and thereforewithout the necessity for transmitting parity bits corresponding to rowsof the zero matrixes to the receiving side, the receiving side insertsknown fixed log likelihood ratios as log likelihood ratios of paritybits corresponding to rows of zero matrixes and can perform decoding,and it is thereby possible to reduce the number of parity bits totransmit and improve transmission efficiency.

The information bits that need to be transmitted are not limited to aheader including control information or the like, but may also bepayload data (symbols for information transmission) or the like. Inshort, the present invention is applicable if the number of informationbits that need to be transmitted is smaller than the number of columnsof zero matrixes included in the QC-LDPC code. When the information bitsthat need to be transmitted are a header and the header length is fixed,zero matrix setting section 110 can set an optimum zero matrix accordingto the header length beforehand.

On the other hand, when the information bits that need to be transmittedare payload data, the data length varies depending on the magnitude ofcontent information or the like. The present invention is alsoapplicable to a case where the data length of information bits that needto be transmitted varies as in the case of payload data. FollowingEmbodiment 2 will describe a case where the data length of informationbits that need to be transmitted varies.

Embodiment 2

The present embodiment will describe a mode in which the presentinvention is applied to a case where the data length of information bitsthat need to be transmitted varies.

FIG. 11 illustrates a configuration example of one block in the casewhere QC-LDPC code is used. The QC-LDPC code is a block code, and asshown in FIG. 11, one block is made up of information bits and paritybits. Here, suppose the number of bits of the information bits in oneblock is M bits.

FIG. 12 illustrates a configuration example of an encoder according tothe present embodiment. In the encoder according to the presentembodiment in FIG. 12, the same components as those in FIG. 6 will beassigned the same reference numerals as those in FIG. 6 and descriptionsthereof will be omitted. Encoder 100 a in FIG. 12 includes zero matrixsetting section 110 a and arrangement section 120 a instead of zeromatrix setting section 110 and arrangement section 120 of encoder 100 inFIG. 6. Hereinafter, a case will be described where an N-bit informationsequence is inputted to encoder 100 a.

Zero matrix setting section 110 a sets a zero matrix according to datalength N of information bits (input bits) inputted as an informationsequence. To be more specific, zero matrix setting section 110 a countsdata length N of the information bits (input bits) first. Zero matrixsetting section 110 a divides data length N by information bit length Mper block of the QC-LDPC code and calculates quotient β and remainder α.

As a result of the division, if N=kM (k is an integer) holds,arrangement section 120 a needs to arrange information bits inputted(input bits), as shown in FIG. 13, in an area of information bits of allk blocks as an information sequence. That is, in k blocks, eachinformation bit (input bit) needs to be arranged in all columns ofparity generator matrix g of the QC-LDPC code. Thus, when N=kM (k is anatural number) holds, zero matrix setting section 110 a does not setany zero matrix but outputs a command signal to arrangement section 120a so as to arrange information bits (input bits) in all columns ofparity generator matrix g.

Thus, when, as a result of the division, N≠kM=βM+α (k is an integer, αand β are natural numbers) holds, arrangement section 120 a needs toarrange information bits (input bits) in areas of information bits of βblocks as shown in FIG. 13 and arrange α information bits (input bits)in an area of information bits of one block (special block). That is,arrangement section 120 a needs to arrange information bits in allcolumns of parity generator matrix g of QC-LDPC code in β blocks andarrange information bits (input bits) in columns of zero matrixes in thespecial block as described in Embodiment 1.

Thus, when N≠kM=βM+α (k, α and β are natural numbers) holds, zero matrixsetting section 110 a sets zero matrixes according to data length α ofinformation bits (input bits) that need to be transmitted in the specialblock. In this case, zero matrix setting section 110 a switches betweenzero matrixes to be set according to the value of data length α. To bemore specific, zero matrix setting section 110 a switches between zeromatrixes to be set according to the comparison result between remainderα and a predetermined threshold. As described above, in encoder 100 a,the maximum value of the number of bits that can be arranged asinformation bits that need to be transmitted varies depending on zeromatrixes.

In FIG. 13, the special block is arranged temporally at the last, butthe arrangement position is not limited to this.

Hereinafter, an operation of setting zero matrixes according to the datalength will be described using FIG. 14. FIG. 14 is an example of thecase where zero matrix setting section 110 a has two thresholds a1 anda2 and switches between zero matrixes according to the comparison resultbetween data length α and the two thresholds. Since the number of paritybits that can be punctured (reduced) as bits not to transmit is the sameas the number of rows of a zero matrix, switching between zero matrixesnamely means switching between methods of reducing parity bits totransmit.

When 0<α≤a1, parity bits to transmit are reduced by zero matrix #1(reduction method #1). When, for example, 0<α≤a1 (=12), zero matrixsetting section 110 a sets zero matrixes 221 and 222 . . . , as zeromatrixes.

When α=10, arrangement section 120 a adds two “0” bits to 10-bitinformation of to obtain 12-bit information. Arrangement section 120 athen assigns 12 bits to x36 to x47 and assigns 0's to x1 to x35 and x48and onward. As a result, parity bits p1 to p7, p28 to p34, . . . of theparity bits obtained from coding section 130 are always 0's regardlessof the values of x36 to x47.

Therefore, when puncturing section (data reducing section) 140 puncturesparity bits p1 to p7, p28 to p34 that are always 0's as bits not totransmit, and can thereby improve transmission efficiency withoutdeteriorating decoding performances.

Furthermore, since known bits “0” are assigned to bits (x1 to x35, x48and onward) other than x36 to x47, puncturing section (data reducingsection) 140 also punctures (sets as bits not to transmit) bits otherthan x36 to x47. In addition, in the case of α=10, puncturing section(data reducing section) 140 punctures (sets as bits not to transmit) thetwo “0” bits assigned to x36 to x47 as bits not to transmit. This makesit possible to further improve transmission efficiency.

When, for example, arrangement section 120 a assigns 0's to x46 and x47,puncturing section (data reducing section) 140 punctures x46 and x47,and the transmission sequence thereby becomes x36 to x45 with parity p8to p27, p35 to p54, . . . , and it is thereby possible to furtherimprove transmission efficiency.

In the case of a1<α≤a2, zero matrix #2 (reduction method #2) reducesparity bits to transmit. For example, in the case of a1=12 and a2=19,zero matrix setting section 110 a sets zero matrixes 231, 232, . . . aszero matrixes in addition to zero matrixes 221 and 222, . . . .

In the case of α=15, arrangement section 120 a adds four “0” bits to15-bit information to obtain 19-bit information. Arrangement section 120a then assigns these 19 bits to x36 to x47 and x71 to x77 and assigns0's to x1 to x35, x48 to x71, x78 and onward. As a result, parity bitsp1 to p7, p28 to p34, . . . of the parity bits obtained by codingsection 130 are always 0's regardless of the values of x36 to x47.

Therefore, puncturing section (data reducing section) 140 puncturesparity bits p1 to p7, p28 to p34 which are always 0's as bits not totransmit, and can thereby improve transmission efficiency withoutdeteriorating decoding performances.

Furthermore, since known bits “0” are assigned to bits (x1 to x35, x48to x71, x78 and onward) other than x36 to x47, x71 to x77, puncturingsection (data reducing section) 140 sets bits other than x36 to x47, x71to x77 as bits to be punctured (bits not to transmit). In addition, inthe case of α=15, puncturing section (data reducing section) 140punctures four “0” bits assigned to x36 to x47, x71 to x77 as bits notto transmit (sets them as bits not to transmit).

This allows the transmitting apparatus to further improve transmissionefficiency. When, for example, arrangement section 120 a assigns 0's tox74 to x77, puncturing section (data reducing section) 140 punctures x74to x77, the transmission sequence thereby becomes x36 to x45, x71 tox73, p8 to p27, p35 to p54, . . . and the transmitting apparatus canthereby further improve transmission efficiency.

In the example shown in FIG. 14, in the case of a2<α≤M−1, no zero matrixis set and parity bits are not reduced. That is, when remainder αresulting from dividing data length N of information bits (input bits)by block length M is equal to or above a predetermined threshold, ainformation bits (input bits) and (M−α) 0's as imaginary bits arearranged in columns of parity generator matrix g.

By this means, zero matrix setting section 110 a sets zero matrixesaccording to data length α of information bits (input bits) that need tobe transmitted in a special block. Zero matrix setting section 110 athen reports information about the positions of zero matrixes in paritygenerator matrix g to arrangement section 120 a and puncturing section(data reducing section) 140.

In the case of a2<α≤M−1, zero matrix setting section 110 a sets no zeromatrixes and reduces no parity bits. Thus, in the case of a2<α≤M−1, zeromatrix setting section 110 a reports puncturing section (data reducingsection) 140 not to puncture parity bits.

As described above, in the present embodiment, zero matrix settingsection 110 a sets zero matrixes which are partial matrixes of paritygenerator matrix g and in which all elements are 0's according to datalength N of information bits (input bits). By so doing, the transmittingapparatus can reduce the number of parity bits that need to betransmitted and reliably transmit information bits (input bits).

FIG. 14 illustrates an example where the method of reducing parity bitsis categorized under one of three cases according to the value ofremainder α but the number of cases is not limited to 3. For example,zero matrix setting section 110 a may be provided with furtherthresholds so that the method is categorized into Z cases.

Furthermore, when implementing the present embodiment, the receivingapparatus provided with the decoder need to know the value of remainderα. A simple method of realizing this may be to cause the transmittingapparatus provided with the encoder to report information about thenumber of bits of data to transmit to the receiving apparatus first. Inthis case, the receiving apparatus needs to be provided with acalculation section to calculate α.

Embodiment 3

The present embodiment will describe a puncturing method of a QC-LDPCcode.

FIG. 15 illustrates a configuration example of an encoder according tothe present embodiment. Encoder 600 in FIG. 15 is provided with codingsection 610, puncturing pattern setting section 620 and puncturingsection (data reducing section) 630.

Coding section 610 performs coding on an information sequence usingparity generator matrix g of QC-LDPC code.

Puncturing pattern setting section 620 searches and sets a puncturingpattern taking advantage of the fact that parity check matrix H ofQC-LDPC code is configured using a subblock matrix as a basic unit. Themethod of searching a puncturing pattern will be described later.Puncturing pattern setting section 620 outputs the information of theset puncturing pattern to puncturing section (data reducing section)630.

Puncturing section (data reducing section) 630 punctures (sets as bitsnot to transmit) information bits or parity bits as bits not to transmitof the coded sequence outputted from coding section 610 according to thepuncturing pattern reported from puncturing pattern setting section 620.

Next, the method of searching a puncturing pattern set by puncturingpattern setting section 620 will be described. A puncturing pattern issearched taking advantage of the fact that parity check matrix H ofQC-LDPC code is configured using a subblock matrix as a basic unit.

When searching a puncturing pattern, puncturing pattern setting section620 determines the cycle of the puncturing pattern first. When, forexample, K bits from the 20th bit are selected as bits not to transmit(puncture bits), the cycle of the puncturing pattern is 20 bits. In thiscase, suppose the number of bits not to transmit (puncture bits)included in 20 bits of the cycle of the puncturing pattern is K andalways constant.

The present invention assumes that the cycle of the puncturing patternis an integer multiple of the number of columns L or a divisor of thenumber of columns L of subblock matrix I(p_(j,1)) (cyclic permutationmatrix of q rows and r columns in which (r=(q+p_(j,1))mod p(0≤q≤p−1) is1 and “0” otherwise) which is a basic unit of the parity check matrix ofQC-LDPC code (see equation 1).

For example, since the subblock matrix in the parity check matrix ofQC-LDPC code shown in FIG. 3 is a matrix of 27 rows and 27 columns(L=27), it is proposed to set an integer multiple of 27 or a divisor of27 as the cycle of the puncturing pattern and set K bits not to transmit(puncture bits).

Generally, the larger the block length, the better receptionperformances are obtained with a block code. However, when the blocklength is large, it is difficult to search a best puncturing pattern inblock length units. Thus, when the block length is large, a scheme ofrandomly selecting a puncture bit may be adopted. However, in this case,there is a possibility that receiving quality may significantlydeteriorate during puncturing.

By contrast, focusing on the regularity with the subblock matrix makingup parity check matrix H of QC-LDPC code, when puncturing patternsetting section 620 searches puncturing patterns every integer multipleof the number of columns or every divisor of the number of columns ofthe subblock matrixes, it is possible to reliably find out a puncturingpattern in which performances become better in a relatively short time.

As a more specific method of searching a puncturing pattern, forexample, a predetermined SNR (Signal-to-Noise power Ratio) may be set,an error rate may be calculated for every puncturing pattern and apuncturing pattern in which the error rate decreases may be determined.

The transmitting apparatus punctures a coded sequence using thepuncturing pattern searched in this way, and can thereby improvetransmission efficiency while maintaining good receiving quality. Thatis, what is important in the configuration in FIG. 15 is that puncturingsection (data reducing section) 630 punctures a coded sequence using aninteger multiple of the number of columns or a divisor of the number ofcolumns of subblock matrixes making up parity check matrix H of QC-LDPCcode as a unit.

A case will be described as an example where puncturing section (datareducing section) 630 assumes the cycle of the puncturing pattern as thenumber of columns L of the subblock matrix and sets the number of bitsnot to transmit (puncture bits) to constant number K for every number ofcolumns L of the subblock matrix. In this case, puncturing section (datareducing section) 630 switches between puncturing patterns every integermultiple of the number of columns of a subblock matrix making up paritycheck matrix H of QC-LDPC code.

The method of switching between puncturing patterns will be describedmore specifically using FIG. 16A to FIG. 16C.

FIG. 16A illustrates a situation in which a puncturing pattern isswitched every number of columns (one time of the number of columns) ofa subblock matrix for parity check matrix H in FIG. 3. Since paritycheck matrix H in FIG. 3 is made up of subblock matrixes of 27 columns,puncturing section (data reducing section) 630 selects K bits not totransmit (puncture bits) using puncturing pattern #0 for x1 to x27.Furthermore, puncturing section (data reducing section) 630 selects Kbits not to transmit (puncture bits) using puncturing pattern #1 for x28to x54. Furthermore, puncturing section (data reducing section) 630selects K bits not to transmit (puncture bits) using puncturing pattern#23 for p622 to p648.

FIG. 16B illustrates a situation in which a puncturing pattern isswitched every two times the number of columns of subblock matrix forparity check matrix H in FIG. 3. Since parity check matrix H in FIG. 3is made up of a subblock matrix of 27 columns, puncturing section (datareducing section) 630 selects K bits not to transmit (puncture bits)using puncturing pattern #0 for x1 to x27, x28 to x54.

Furthermore, puncturing section (data reducing section) 630 selects Kbits not to transmit (puncture bits) using puncturing pattern #1 for x55to x81, x82 to x108. Furthermore, puncturing section (data reducingsection) 630 selects K bits not to transmit (puncture bits) usingpuncturing pattern #2 for x109 to x135, x136 to x162.

FIG. 16C illustrates a situation in which a puncturing pattern isswitched for every 9 columns based on a base cycle of 9 columns, whichis a divisor of the number of columns of the subblock matrix for paritycheck matrix H in FIG. 3. To be more specific, puncturing section (datareducing section) 630 selects K bits not to transmit (puncture bits)using puncturing pattern #0 for x1 to x9.

Puncturing section (data reducing section) 630 selects K bits not totransmit (puncture bits) using puncturing pattern #1 for x10 to x18.Puncturing section (data reducing section) 630 selects K bits not totransmit (puncture bits) using puncturing pattern #2 for x19 to x27.

Likewise, puncturing section (data reducing section) 630 selects K bitsnot to transmit (puncture bits) using puncturing pattern #3 for x28 tox36. Puncturing section (data reducing section) 630 selects K bits notto transmit (puncture bits) using puncturing pattern #4 for x37 to x45.Puncturing section (data reducing section) 630 selects K bits not totransmit (puncture bits) using puncturing pattern #5 for x46 to x54.

Likewise, puncturing section (data reducing section) 630 selects K bitsnot to transmit (puncture bits) using puncturing pattern #69 for x622 tox630. Puncturing section (data reducing section) 630 selects K bits notto transmit (puncture bits) using puncturing pattern #70 for x631 tox639. Puncturing section (data reducing section) 630 selects K bits notto transmit (puncture bits) using puncturing pattern #71 for x640 tox648.

Puncturing section (data reducing section) 630 defines puncturingpattern #S0 made up of puncturing patterns #0 to #2 selects 3K bits notto transmit (puncture bits) using puncturing pattern #S0 for x1 to x27.Likewise, puncturing section (data reducing section) 630 may also definepuncturing pattern #S1 made up of puncturing patterns #3 to #5 andselect 3K bits not to transmit (puncture bits) using puncturing pattern#S1 for x28 to x54.

Likewise, puncturing section (data reducing section) 630 may also definepuncturing pattern #S23 made up of puncturing patterns #69 to #71 andselect 3K bits not to transmit (puncture bits) using puncturing pattern#S23 for x622 to x648.

That is, performing puncturing by using a divisor of the number ofcolumns of the subblock matrix as the base cycle is equivalent toperforming puncturing using the number of columns of the subblock matrixmaking up parity check matrix H of QC-LDPC code as a unit (cycle).

As described so far, in the present embodiment, puncturing patternsetting section 620 searches a puncturing pattern for every integermultiple of the number of columns or every divisor of the number ofcolumns of subblock matrixes making up parity check matrix H of QC-LDPCcode and puncturing section (data reducing section) 630 switches betweenpuncturing patterns for every integer multiple of the number of columnsor every divisor of the number of columns of subblock matrixes making upthe parity check matrix of QC-LDPC code. This makes it possible tosearch a puncturing pattern whereby good receiving quality is obtainedin a relatively short time and reliably, and improve transmissionefficiency while maintaining good receiving quality.

A case has been described above where a puncturing pattern is switchedevery integer multiple of the number of columns or every divisor of thenumber of columns of subblock matrixes making up a parity check matrixof QC-LDPC code, but the puncturing pattern need not always be switched.

For example, in FIG. 16A, “puncturing pattern #0,” “puncturing pattern#1,” . . . , “puncturing pattern #23” may be identical puncturingpatterns. Furthermore, in FIG. 16B, “puncturing pattern #0,” “puncturingpattern #1,” “puncturing pattern #2,” . . . , may be identicalpuncturing patterns.

Furthermore, in FIG. 16C, “puncturing pattern #0,” “puncturing pattern#1,” . . . , “puncturing pattern #71” may be identical puncturingpatterns. In short, the unit of puncturing patterns needs only to be aninteger multiple of the number of columns or a divisor of the number ofcolumns of subblock matrixes making up a parity check matrix of QC-LDPCcode.

Embodiment 4

The present embodiment will describe an example of coding method whenthe coding method described in Embodiment 1 and Embodiment 2 is used forcontrol information.

Hereinafter, a case will be described where 200-bit control informationis coded using a QC-LDPC code of coding rate(R)=1/2, LDPC codeinformation block length (bits)=168, LDPC codeword block length(bits)=336 as an example.

FIG. 17 illustrates a case where 200-bit control information is dividedinto 168 bits and 32 bits, 168 bits are arranged in block #1 and 32 bitsare arranged in block #2. In FIG. 17, only 32 bits of controlinformation are arranged in block #2 in contrast to the block length of168 bits.

Hereinafter, a block such as block #2, bits of which need to betransmitted, is shorter than the block length is the special blockdescribed in Embodiment 2. Thus, as with Embodiment 2, in block #2, 0'sare arranged and coded as information bits as imaginary bits. As aresult, there is a variation in receiving quality between block #1 andblock #2 and receiving quality of 200-bit control information eventuallydepends on blocks having poor receiving quality.

Thus, as shown in FIG. 18, the present embodiment arranges 200-bitcontrol information in two blocks #1 and #2 as uniformly as possible andperforms the coding described in Embodiment 1 on each block. To be morespecific, when the control information has 200 bits, control informationis arranged in both block #1 and block #2, 100 bits each.

This causes both block #1 and block #2 to become special blocks, andtherefore 0's are arranged in both block #1 and block #2 as informationbits as imaginary bits and coded using the coding method according toEmbodiment 1. This makes receiving quality uniform in block #1 and block#2 and allows signals to be transmitted correctly to the communicatingparty.

When control information has 201 bits, 101 bits of control informationare arranged in block #1 and 100 bits of control information arearranged in block #2. In this case, the difference between the number ofbits of control information in block #1 and the number of bits ofcontrol information in block #2 is one bit at most. Thus, thetransmitting apparatus arranges information that needs to be transmittedin two blocks as uniformly as possible, and can thereby make receivingquality uniform between the blocks, and can thereby reliably transmitcontrol information to the communicating party.

As described so far, the present embodiment arranges control informationin a plurality of blocks as uniformly as possible. Thus, thetransmitting apparatus applies the coding method described in Embodiment1 to each block after the arrangement, and can thereby reliably transmitinformation necessary to establish communication such as controlinformation to the communicating party.

The method of generating a special block according to the presentembodiment is the same as the method of generating a special blockdescribed in Embodiment 2. That is, the transmitting apparatus sets(sets as puncture bits) both information bits and parity bits that neednot be transmitted as bits not to transmit.

Embodiment 5

The present embodiment will show an example of QC-LDPC code and describean optimum puncturing pattern for the QC-LDPC code.

Parity check matrix H of QC-LDPC code is defined as shown in equation 4.

$\begin{matrix}{\mspace{85mu}\lbrack 4\rbrack} & \; \\{H = {\begin{bmatrix}P_{0,0} & P_{0,1} & P_{0,2} & \ldots & P_{0,{n_{b} - 2}} & P_{0,{n_{b} - 1}} \\P_{1,0} & P_{1,1} & P_{1,2} & \ldots & P_{1,{n_{b} - 2}} & P_{1,{n_{b} - 1}} \\P_{2,0} & P_{2,1} & P_{2,2} & \ldots & P_{2,{n_{b} - 2}} & P_{2,{n_{b} - 1}} \\\vdots & \vdots & \vdots & \ldots & \vdots & \vdots \\P_{{m_{b} - 1},0} & P_{{m_{b} - 1},1} & P_{{m_{b} - 1},2} & \ldots & P_{{m_{b} - 1},{n_{b} - 2}} & P_{{m_{b} - 1},{n_{b} - 1}}\end{bmatrix} = P^{H_{b}}}} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$

Parity check matrix H in equation 4 is a matrix of m rows and n columns.Here, n denotes a code length and m denotes the number of parity bits.Therefore, the number of systematic bits k is k=n−m. Furthermore,P_(i,j) in equation 4 is a cyclic permutation matrix of z rows and zcolumns or a zero matrix of z rows and z columns.

Here, parity check matrix H in equation 4 is expanded with matrix H_(b)of n_(b) rows and m_(b) columns. Here, the relationships m=z×m_(b) andn=z×n_(b) hold. Furthermore, suppose each element of matrix H_(b) is “1”when each element of P_(i,j) is “1” and “0” when each element of P_(i,j)is “0.”

Here, as a cyclic permutation matrix, P_(i,j) is a unit matrix of z rowsand z columns or a set of matrixes cyclically shifting a unit matrix ofz rows and z columns. Since the cyclic permutation matrix is a unitmatrix or a set of matrixes cyclically shifting a unit matrix, whenmatrix H_(b) is divided into matrix H_(bm) having the same magnitude asmatrix H_(b), matrix H_(bm) is represented by zero matrixes or matrixescyclically shifting a unit matrix.

Hereinafter, a zero matrix in matrix H_(bm) will be represented as “−1.”Furthermore, suppose the unit matrix is represented as “0.” Furthermore,the cyclic permutation matrix of the unit matrix is represented as“p(i,j)” using an amount of cyclic shift thereof p(i,j) (>0). MatrixH_(b) can be represented as a set of such compactly represented matrixesH_(bm).

Here, as shown in equation 5, matrix H_(b) can be divided into twosubmatrixes H_(b1) and H_(b2). Submatrix H_(b1) is a partial matrixrelated to information bits and submatrix H_(b2) is a partial matrixrelated to parity bits.

[5]H _(b)=[(H _(b1))_(mb×kb)|(H _(b2))_(mb×mb)]=0  (Equation 5)

As shown in equation 6, submatrix H_(b2) is further divided into vectorh_(b) and submatrix H′_(b2).

$\begin{matrix}\lbrack 6\rbrack & \; \\{H_{b\; 2} = {\left\lbrack h_{b} \middle| H_{b\; 2}^{\prime} \right\rbrack = \begin{bmatrix}{h_{b}(0)} & | & 1 & \; & \; & \; & \; \\{h_{b}(1)} & | & 1 & 1 & \; & 0 & \; \\\ldots & | & \; & 1 & \ddots & \; & \; \\\ldots & | & \; & \; & \ddots & 1 & \; \\\ldots & | & \; & 0 & \; & 1 & 1 \\{h_{b}\left( {m_{b} - 1} \right)} & | & \; & \; & \; & \; & 1\end{bmatrix}}} & \left( {{Equation}\mspace{14mu} 6} \right)\end{matrix}$

In equation 6, submatrix H′_(b2) is a matrix in which portions of thei-th row and j-th column (i=j and i=j+1) are “1” and the other portionsare “0.” In submatrix H′_(b2), portions represented as “1” indicate thatthe amount of shift of unit matrixes is 0. That is, submatrix H′_(b2) isreplaced by unit matrixes of z rows and z columns when expanded tomatrix H_(b).

Furthermore, suppose the same amount of cyclic shift is assigned to thetop (h_(b)(0)) and bottom (h_(b)(m_(b)−1)) of vector h_(b).

Hereinafter, matrix H_(b) defined by equation 7 will be considered.Parity check matrix H defined by equation 7 can correspond to a maximumcode length at each coding rate.

$\begin{matrix}\lbrack 7\rbrack & \; \\{{p\left( {f,i,j} \right)} = \left\{ {\begin{matrix}{{p\left( {i,j} \right)},} & {{p\left( {i,j} \right)} \leq 0} \\{\left\lfloor {{p\left( {i,j} \right)} \cdot \frac{z_{f}}{96}} \right\rfloor,} & {{p\left( {i,j} \right)} > 0}\end{matrix}{where}\mspace{20mu}\left\lfloor {{p\left( {i,j} \right)} \cdot \frac{z_{f}}{96}} \right\rfloor} \right.} & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$represents the integer portion of

${p\left( {i,j} \right)} \cdot {\frac{z_{f}}{96}.}$

In equation 7, p(f,i,j) denotes the amount of cyclic shift of the unitmatrix, f denotes an index of code length corresponding to each codingrate. Furthermore, z_(f) is called “expansion factor” and has therelationship of z_(f)=k/n.

Equation 8 expresses matrix H_(b) of coding rate 1/2(=k/n) based onequation 7.

$\begin{matrix}{\mspace{79mu}\lbrack 8\rbrack} & \; \\\begin{matrix}{- 1} & 94 & 73 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 55 & 83 & {- 1} & {- 1} & 7 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 27 & {- 1} & {- 1} & {- 1} & 22 & 79 & 9 & {- 1} & {- 1} & {- 1} & 12 & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & {- 1} & {- 1} & 24 & 22 & 81 & {- 1} & 33 & {- 1} & {- 1} & {- 1} & 0 & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\61 & {- 1} & 47 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 65 & 25 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & {- 1} & 39 & {- 1} & {- 1} & {- 1} & 84 & {- 1} & {- 1} & 41 & 72 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & {- 1} & {- 1} & {- 1} & 46 & 40 & {- 1} & 82 & {- 1} & {- 1} & {- 1} & 79 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & {- 1} & 95 & 53 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 14 & 18 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 11 & 73 & {- 1} & {- 1} & {- 1} & 2 & {- 1} & {- 1} & 47 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} \\12 & {- 1} & {- 1} & {- 1} & 83 & 24 & {- 1} & 43 & {- 1} & {- 1} & {- 1} & 51 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} \\{- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 94 & {- 1} & 59 & {- 1} & {- 1} & 70 & 72 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} \\{- 1} & {- 1} & 7 & 65 & {- 1} & {- 1} & {- 1} & {- 1} & 39 & 49 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 0 & 0 \\43 & {- 1} & {- 1} & {- 1} & {- 1} & 66 & {- 1} & 41 & {- 1} & {- 1} & {- 1} & 26 & 7 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 0\end{matrix} & \left( {{Equation}\mspace{14mu} 8} \right)\end{matrix}$

In equation 8, “0” represents a unit matrix. On the other hand, “−1”represents a zero matrix. Furthermore, “94” on the first row and thesecond column represents a matrix cyclically shifting the unit matrix by94. Likewise, “61” on the fourth row and the first column represents amatrix cyclically shifting the unit matrix by 61.

Furthermore, equation 9 expresses matrix H_(b) of coding rate 5/6(=k/n)based on equation 7.

$\begin{matrix}{\mspace{79mu}\lbrack 9\rbrack} & \; \\\begin{matrix}1 & 25 & 55 & {- 1} & 47 & 4 & {- 1} & 91 & 84 & 8 & 86 & 52 & 62 & 33 & 5 & 0 & 36 & 20 & 4 & 77 & 80 & 0 & {- 1} & {- 1} \\{- 1} & 6 & {- 1} & 36 & 40 & 47 & 12 & 79 & 47 & {- 1} & 41 & 21 & 12 & 71 & 14 & 72 & 0 & 44 & 49 & 0 & 0 & 0 & 0 & {- 1} \\51 & 3 & 83 & 4 & 67 & {- 1} & 21 & {- 1} & 31 & 24 & 91 & 61 & 31 & 9 & 86 & 78 & 60 & 88 & 67 & 15 & {- 1} & {- 1} & 0 & 0 \\50 & {- 1} & 50 & 15 & {- 1} & 36 & 13 & 10 & 11 & 20 & 53 & 90 & 29 & 92 & 57 & 30 & 34 & 92 & 11 & 66 & 30 & {- 1} & {- 1} & 0\end{matrix} & \left( {{Equation}\mspace{14mu} 9} \right)\end{matrix}$

An example of matrix H_(b) of QC-LDPC code of coding rates 1/2 and 5/6has been shown above. Hereinafter, a puncturing pattern applicable tomatrix H_(b) of QC-LDPC code will be described.

FIG. 19A illustrates matrix H_(b) of QC-LDPC code of coding rate 1/2shown in equation 8. As shown in FIG. 19A, in matrix H_(b) of codingrate 1/2, since partial matrix H_(b1) related to information bits has 12rows, partial matrix H_(b2) related to parity bits has 12 columns.

Partial matrix H_(b2) related to parity bits in FIG. 19A is made up of“−1” and “0” except for the first row, first column and 12th row, firstcolumn and has a regular arrangement. As described above, “−1”represents a zero matrix and “0” represents a unit matrix. Furthermore,“7” on the first row, first column and 12th row, first column is acyclic permutation matrix cyclically shifting the unit matrix by 7.

In this case, portions made up of unit matrixes and zero matrixes incolumns of partial matrix H_(b2) related to parity bits have a smalleffect on receiving quality even if the same puncturing pattern is used.Therefore, it is possible to obtain good reception characteristics fromthe portions made up of unit matrixes and zero matrixes even if the samepuncturing pattern #A is used (see FIG. 19A). Suppose differentpuncturing patterns are set for portions not corresponding to theportions made up of unit matrixes and zero matrixes. However, some orall puncturing patterns may be the same puncturing pattern.

Furthermore, the coded sequence may also be combined with the puncturingmethod described in Embodiment 3. That is, it is further effective ifthe coded sequence is punctured using an integer multiple of the numberof columns or a divisor of the number of columns of subblock matrixesmaking up parity check matrix H of QC-LDPC code as a unit. FIG. 19B andFIG. 19C illustrate examples where partial matrix H_(b2) related toparity bits is punctured using an integer multiple of the number ofcolumns or a divisor of the number of columns of subblock matrixesmaking up parity check matrix H of QC-LDPC code as the unit.

FIG. 19B illustrates another application example of matrix H_(b) ofQC-LDPC code of coding rate 1/2 shown in equation 8 and puncturingpatterns. FIG. 19B is an example of the case where the cycle of puncturepattern is set to an integer multiple (two times) of the number ofcolumns of subblock matrixes making up the parity check matrix ofQC-LDPC code. FIG. 19B is an example where the same puncturing pattern#B is used for portions made up of unit matrixes and zero matrixes.

Furthermore, FIG. 19C illustrates a further application example ofmatrix H_(b) of QC-LDPC code of coding rate 1/2 shown in equation 8 andpuncturing patterns. FIG. 19C is an example where a puncturing patternis generated for every 1/2 of the number of columns of subblock matrixesmaking up the parity check matrix of QC-LDPC code. FIG. 19C is anexample of the case where the same puncturing pattern is used forportions made up of unit matrixes and zero matrixes.

To be more specific, FIG. 19C illustrates a situation in which apuncturing pattern is switched for every 50 columns for parity checkmatrix H made up of subblock matrixes of 100 rows and 100 columns basedon a base cycle of 50 columns, which is a divisor half the number ofcolumns of the subblock matrix.

To be more specific, puncturing section (data reducing section) 630selects bits not to transmit (puncture bits) for p100 to p149 usingpuncturing pattern #1. Puncturing section (data reducing section) 630selects bits not to transmit (puncture bits) for p150 to p199 usingpuncturing pattern #2. Puncturing section (data reducing section) 630selects bits not to transmit (puncture bits) for p200 to p249 usingpuncturing pattern #3.

Puncturing section (data reducing section) 630 selects bits not totransmit (puncture bits) for p250 to p299 using puncturing pattern #4.Puncturing section (data reducing section) 630 selects bits not totransmit (puncture bits) for p1100 to p1149 using puncturing pattern#21. Puncturing section (data reducing section) 630 selects bits not totransmit (puncture bits) for p1150 to p1199 using puncturing pattern#22.

FIG. 20A illustrates matrix H_(b) of QC-LDPC code of coding rate 5/6shown in equation 9. As shown in FIG. 20A, since parity check matrixH_(b) of coding rate 5/6 has partial matrix H_(b1) of 4 rows related toinformation bits, partial matrix H_(b2) related to parity bits have 4columns.

Partial matrix H_(b2) related to parity bits in FIG. 20A is made up of“−1” and “0” except for the first row, first column and the fourth row,first column, and has a regular arrangement. Furthermore, “80” on thefirst row, first column and the fourth row, first column is a cyclicpermutation matrix cyclically shifting the unit matrix by 80.

Thus, in the case of coding rate 5/6, even when the same puncturingpattern is used for portions made up of unit matrixes and zero matrixesin the columns of partial matrix H_(b2) related to parity bits,influences on receiving quality are small. Thus, the receiving apparatuscan obtain good reception characteristics for columns of the portionsmade up of unit matrixes and zero matrixes using also the samepuncturing pattern #A (see FIG. 20A). The columns not related to theportions made up of unit matrixes and zero matrixes may be set todifferent puncturing patterns, but may also be set to partiallyidentical puncturing patterns. FIG. 20B illustrates another applicationexample of matrix H_(b) of QC-LDPC of coding rate 5/6 shown in equation9 and puncturing patterns. FIG. 20B is an example where the cycle ofpuncturing pattern is set to an integer multiple (3 times) of the numberof columns of subblock matrixes making up the parity check matrix ofQC-LDPC code.

Furthermore, FIG. 20C illustrates a further application example ofmatrix H_(b) of QC-LDPC code of coding rate 5/6 shown in equation 9 andpuncturing patterns. FIG. 20C is an example of the case where apuncturing pattern is generated for every 1/2 of the number of columnsof subblock matrixes making up the parity check matrix of QC-LDPC code.As with FIG. 20B, FIG. 20C is an example where the same puncturingpattern is used for portions made up of unit matrixes and zero matrixes.

To be more specific, FIG. 20C illustrates a situation in which apuncturing pattern is switched for every 50 columns for parity checkmatrix H made up of subblock matrixes of 100 rows and 100 columns basedon a base cycle of 50 columns, which is a divisor half the number ofcolumns of the subblock matrix.

To be more specific, puncturing section (data reducing section) 630selects bits not to transmit (puncture bits) for p100 to p149 usingpuncturing pattern #1. Puncturing section (data reducing section) 630selects bits not to transmit (puncture bits) for p150 to p199 usingpuncturing pattern #2. Puncturing section (data reducing section) 630selects bits not to transmit (puncture bits) for p200 to p249 usingpuncturing pattern #3.

Puncturing section (data reducing section) 630 selects bits not totransmit (puncture bits) for p250 to p299 using puncturing pattern #4.Puncturing section (data reducing section) 630 selects bits not totransmit (puncture bits) for p300 to p349 using puncturing pattern #5.Puncturing section (data reducing section) 630 selects bits not totransmit (puncture bits) for p350 to p399 using puncturing pattern #6.

Thus, the portions made up of unit matrixes and zero matrixes of thecolumns in partial matrix H_(b2) related to parity bits are set to thesame puncturing pattern and the columns not related to the portions madeup of unit matrixes and zero matrixes are set to different puncturingpatterns.

A puncturing pattern may also be switched for the columns not related tothe portions made up of unit matrixes and zero matrixes for everyinteger multiple of the number of columns or every divisor of the numberof columns of subblock matrixes making up the parity check matrix ofQC-LDPC code as described, for example, in Embodiment 3.

Furthermore, the same puncturing pattern whose pattern lengthcorresponds to every integer multiple of the number of columns or everydivisor of the number of columns of subblock matrixes making up theparity check matrix of QC-LDPC code may be applied to the columns notrelated to the portions made up of unit matrixes and zero matrixes.

Embodiment 6

An example will be described where the QC-LDPC code described inEmbodiment 5 is used, puncturing is performed using an integer multipleof the number of columns or a divisor of the number of columns ofsubblock matrixes making up the parity check matrix of QC-LDPC codedescribed in Embodiment 4 as a unit and the same puncturing pattern isused for all.

Embodiment 6 will describe a puncturing pattern for realizing a codingrate of approximately 0.65 through puncturing from a QC-LDPC code havingthe parity check matrix of equation 8 of coding rate 1/2. However,suppose the size of subblock matrixes making up the parity check matrixof QC-LDPC code is 350 rows and 350 columns. Therefore, the informationblock length (bits) of QC-LDPC code is 4200 and the LDPC codeword blocklength (bits) is 8400.

In this case, a codeword of the LDPC code is expressed as follows:

$\begin{matrix}{v = \left\lbrack {{x\; 0},{x\; 1},\ldots\;,{x\; 4198},{x\; 4199},{p\; 0},{p\; 1},\ldots\;,{p\; 4198},{p\; 4199}} \right\rbrack} \\{= \left\lbrack {{s\; 0},{s\; 1},{s\; 2},\ldots\;,{s\; 8397},{s\; 8398},{s\; 8399}} \right\rbrack} \\{= \left\lbrack {{v\; 0},{v\; 1},{v\; 2},\ldots\;,{v\; 167}} \right\rbrack}\end{matrix}$where v denotes a codeword, x denotes information and p denotes parity.

v0, v1, . . . , vi . . . , v167 can be expressed as follows:

v0=[s0, s1, . . . , s48, s49],

v1=[s50, s51, . . . , s98, s99], . . . ,

vi=[s50*i, s50*i+1, . . . , s50*i+48, s50*i+49], . . . ,

v167=[s8350, s8351, . . . , s8398, s8399]

As a result of searching a puncturing pattern, the present inventorshave confirmed that good receiving quality is provided if 50 which isthe divisor of the number of columns of subblock matrixes making up theparity check matrix of QC-LDPC code is assumed to be the cycle of thepuncturing pattern.

The puncturing pattern that provides good receiving quality is asfollows:

(1, 8, 19, 20, 25, 28, 29, 31, 38, 40, 41)

As another expression, puncture table w can be expressed as:

w=[1011111101 1111111110 0111101100 1011111101 0011111111]

In this case, 0's included in w denote bits not to transmit. That is,puncture table w determines bits not to transmit as shown in FIG. 21with respect to vi. Therefore, data bit vi′ to be transmitted except forbits not to transmit with respect to vi=[s50*i, s50*i+1, . . . ,s50*i+48, s50*i+49] is represented by:

vi′=[s50*i, s50*i+2, s50*i+3, s50*i+4, s50*i+5, s50*i+6, s50*i+7,s50*i+9, s50*i+10, s50*i+11, s50*i+12, s50*i+13, s50*i+14, s50*i+15,s50*i+16, s50*i+17, s50*i+18, s50*i+21, s50*i+22, s50*i+23, s50*i+24,s50*i+26, s50*i+27, s50*i+30, s50*i+32, s50*i+33, s50*i+34, s50*i+35,s50*i+36, s50*i+37, s50*i+39, s50*i+42, s50*i+43, s50*i+44, s50*i+45,s50*i+46, s50*i+47, s50*i+48, s50*i+49]

A puncturing pattern for realizing a coding rate of approximately 0.95through puncturing from QC-LDPC code having the parity check matrix inequation 9 of coding rate 5/6 will be described. Here, suppose the sizeof subblock matrixes making up the parity check matrix of QC-LDPC codeis 210 rows and 210 columns. Therefore, in the QC-LDPC code, theinformation block length (bits) is 4200 and the LDPC codeword blocklength (bits) is 5040.

In this case, a codeword of the LDPC code is expressed as follows:

$\begin{matrix}{v = \left\lbrack {{x\; 0},{x\; 1},\ldots\;,{x\; 4198},{x\; 4199},{p\; 0},{p\; 1},\ldots\;,{p\; 838},{p\; 839}} \right\rbrack} \\{= \left\lbrack {{s\; 0},{s\; 1},{s\; 2},\ldots\;,{s\; 5037},{s\; 5038},{s\; 5039}} \right\rbrack} \\{= \left\lbrack {{v\; 0},{v\; 1},{v\; 2},\ldots\;,{v\; 79}} \right\rbrack}\end{matrix}$where v denotes a codeword, x denotes information and p denotes parity.

v0, v1, . . . , vi . . . , v79 can be expressed as follows:

v0=[s0, s1, . . . , s61, s62],

v1=[s63, s64, . . . , s124, s125], . . . ,

vi=[s63*i, s63*i+1, . . . , s63*i+61, s63*i+62], . . . ,

v79=[s4977, s4978, . . . , s5038, s5039]

As a result of searching a puncturing pattern, the present inventorshave confirmed that good receiving quality is provided if 63 is assumedto be the cycle of the puncturing pattern.

The puncturing pattern that provides good receiving quality is asfollows:

(3, 18, 20, 27, 39, 50, 60)

As another expression, puncture table w can be expressed as:

w=[1110111111 1111111101 0111111011 1111111110 1111111111 0111111111011]

In this case, 0's included in w means bits not to transmit. That is,with respect to vi, puncture table w determines bits not to transmit asshown in FIG. 22. Therefore, with respect to vi=[s63*i, s63*i+1,s63*i+61, s63*i+62], data bits vi′ to be transmitted, not including bitsnot to be transmitted, can be expressed as:

vi′=[s63*i, s63*i+1, 63*i+2, s63*i+4, s63*i+5, s63*i+6, s63*i+7,s63*i+8, 63*i+9, s63*i+10, s63*i+11, s63*i+12, s63*i+13, s63*i+14,s63*i+15, s63*i+16, s63*i+17, s63*i+19, s63*i+21, s63*i+22, s63*i+23,s63*i+24, s63*i+25, s63*i+26, s63*i+28, s63*i+29, s63*i+30, s63*i+31,s63*i+32, s63*i+33, s63*i+34, s63*i+35, s63*i+36, s63*i+37, s63*i+38,s63*i+40, s63*i+41, s63*i+42, s63*i+43, s63*i+44, s63*i+45, s63*i+46,s63*i+47, s63*i+48, s63*i+49, s63*i+51, s63*i+52, s63*i+53, s63*i+54,s63*i+55, s63*i+56, s63*i+57, s63*i+58, s63*i+59, s63*i+61, s63*i+62]

In this case, if the cycle of the puncturing pattern is assumed to be onthe order of 20 to 90, data quality when received is improved. The“cycle of a puncturing pattern” refers to the minimum cycle of thepuncturing pattern. For example, the puncturing pattern cycle ofpuncture table w1=[001] is 3. Furthermore, puncture table w2=[001001]has a configuration with cycle 6 and is made up of two puncture tablesw1=[001], and since the puncturing pattern cycle of puncture table w1 is3, the (minimum) puncturing pattern cycle of puncture table w2 is 3 aswith puncture table w1. That is, the cycle of a puncturing patternrefers to the pattern length of a minimum one of patterns making up thepuncturing pattern. Furthermore, though puncture table w3=[010] isidentical to one cyclically shifting w1, when the above describedrelationship between w, vi and vi′ is taken into account, w3 and w1 canbe said to be different puncturing patterns. That is, when puncturetable wx and puncture table wy are given, even if wx is cyclicallyshifted (not including 0-bit cyclic shifting) and becomes identical towy, wx and wy are still different puncturing patterns.

When the cycle of a puncturing pattern is too long, irregularity occursin the arrangement of bits not to transmit (puncture bits), whichbecomes similar to a model in which a random error has occurred in abinary erasure channel, causing data quality to become poor duringreception. On the other hand, when the cycle of a puncturing pattern istoo short, the arrangement of bits not to transmit (puncture bits) isunbalanced, the puncturing pattern is less likely to be adequate anddata quality becomes poor during reception. For this reason, it isimportant to set the cycle of the puncturing pattern to the order of 20to 90.

Furthermore, when the cycle of a puncturing pattern is set to the orderof 20 to 90, if three or more 0's are included in puncture table w, thedata quality during reception becomes good (it is more likely to be ableto generate a puncturing pattern whereby high data quality can beobtained during reception (decoding)). When three or more 0's areincluded in puncture table w, the arrangement of bits not to transmit(puncture bits) is no longer regular and randomness increases, and,consequently, data quality during reception becomes good.

Moreover, if the cycle of the puncturing pattern is set to the order of20 to 90, three or more 0's are included in puncture table w and aninteger multiple of the number of columns or a divisor of the number ofcolumns of subblock matrixes making up the parity check matrix ofQC-LDPC code is set as the cycle of the puncturing pattern, it is morelikely to be able to generate a puncturing pattern whereby high dataquality can be obtained during reception (decoding).

Other puncturing patterns include the following: Assuming the size ofsubblock matrixes making up the parity check matrix of QC-LDPC code is80 rows and 80 columns, puncturing patterns for realizing coding ratesof approximately 0.65 and 0.75 through puncturing from QC-LDPC code(information block length (bits)=960, LDPC codeword block length(bits)=1920) having the parity check matrix of equation 8 of coding rate1/2 are as follows:

When coding rate is approximately 0.65: w=[1111110110 0100111111]

When coding rate is approximately 0.75: w=[1100111111 11011111100111110001 1110000111]

Assuming the size of subblock matrixes making up the parity check matrixof QC-LDPC code is 48 rows and 48 columns, a puncturing pattern forrealizing a coding rate of approximately 0.95 through puncturing fromQC-LDPC code (information block length (bits)=960, LDPC codeword blocklength (bits)=1152) having the parity check matrix of equation 9 ofcoding rate 5/6 is as follows:

w=[1111111110 1111111111 0111101111 1111001111 11101111]

Assuming the size of subblock matrixes making up the parity check matrixof QC-LDPC code is 180 rows and 180 columns, puncturing patterns forrealizing coding rates of approximately 0.65 and 0.75 through puncturingfrom QC-LDPC code (information block length (bits)=2160, LDPC codewordblock length (bits)=4320) having the parity check matrix of equation 8of coding rate 1/2 are as follows:

When coding rate is approximately 0.65: w=[1011111100 00111111011111100111 011111]

When coding rate is approximately 0.75: w=[1111110100 00011010011111111110]

Assuming the size of subblock matrixes making up the parity check matrixof QC-LDPC code is 108 rows and 108 columns, a puncturing pattern forrealizing a coding rate of approximately 0.95 through puncturing fromQC-LDPC code (information block length (bits)=2160, LDPC codeword blocklength (bits)=2592) having the parity check matrix of equation 9 ofcoding rate 5/6 is as follows:

w=[1011111111 1111011111 1110111]

Embodiment 7

Embodiment 5 has described the case where different puncturing patternsare used in parity check matrix H_(b), between submatrix H′_(b2) (seeequation 6) made up of unit matrixes and zero matrixes and submatrixesother than submatrix H′_(b2) (hereinafter represented as“H′_(b1)(=H_(b1)+h_(b))”), see equations 5 and 6). As an examplethereof, as shown in FIG. 19A to FIG. 19C, FIG. 20A to FIG. 20C,Embodiment 5 has described a case where identical puncturing patternsare used for submatrix H′_(b2) made up of unit matrixes and zeromatrixes using an integer multiple of the number of columns or a divisorof the number of columns of subblock matrixes as a unit.

As with Embodiment 5, the present embodiment will describe a case wheredifferent puncturing patterns will be used for submatrix H′_(b2) made upof unit matrixes and zero matrixes, and submatrix H′_(b1) in paritycheck matrix H_(b). To be more specific, as shown in FIG. 23 whichcorresponds to FIG. 20B, a case will be described where a coding rate of20/21 is realized using puncturing pattern #p1 whose puncture cycle isthe number of columns of submatrix H′_(b1) for submatrix H′_(b1) andusing puncturing pattern #p2 whose puncture cycle is the number ofcolumns of submatrix H′_(b2) for submatrix H′_(b2).

Hereinafter, a puncturing pattern for realizing coding rate 20/21through puncturing from a QC-LDPC code having a parity check matrix ofequation 9 of coding rate 5/6 will be described as an example.

Parity check matrix H_(b) in FIG. 24 is parity check matrix H_(b) ofQC-LDPC of coding rate 5/6 shown in equation 9. Parity check matrixH_(b) in equation 9 is made up of a subblock matrix of 4 rows and 24columns. Hereinafter, suppose the size of subblock matrixes making upthe parity check matrix of QC-LDPC code is 48 rows and 48 columns.Therefore, in the QC-LDPC code, the information block length (bits) is960 and the LDPC codeword block length (bits) is 1152.

In this case, a codeword of the LDPC code is expressed as follows:

$\begin{matrix}{v = \left\lbrack {{x\; 0},{x\; 1},\ldots\;,{x\; 958},{x\; 959},{p\; 0},{p\; 1},\ldots\;,{p\; 190},{p\; 191}} \right\rbrack} \\{= \left\lbrack {{s\; 0},{s\; 1},{s\; 2},\ldots\;,{s\; 1149},{s\; 1150},{s\; 1151}} \right\rbrack} \\{= \left\lbrack {{v\; 0},{v\; 1},{v\; 2},\ldots\;,{v\; 24}} \right\rbrack}\end{matrix}$where v denotes a codeword, x denotes information and p denotes parity.

v0, v1, . . . , vi . . . , v23 can be expressed as follows:

v0=[s0, s1, . . . , s46, s47],

v1=[s48, s48, . . . , s94, s95], . . . ,

vi=[s48*i, s48*i+1, . . . , s48*i+46, s48*i+47], . . . ,

v23=[s1104, s1105, . . . , s1150, s1151]

In FIG. 24, #0 represents a partial matrix corresponding to x0, x1, . .. , x47 and #1 represents a partial matrix corresponding to x48, x49, .. . , x95. Furthermore, #21 represents a partial matrix corresponding top48, p49, . . . , p95, #22 represents a partial matrix corresponding top96, p97, . . . , p143 and #23 represents a partial matrix correspondingto p144, p145, . . . , p191.

In FIG. 24, submatrix H′_(b1) is made up of #0 to 20 and submatrixH′_(b2) is made up of #21, #22 and #23. #21, #22 and #23 are made up ofunit matrixes (“0”) and zero matrixes (“−1”). Thus, parity check matrixH_(b) of the QC-LDPC code expressed in equation 9 includes submatrixH′_(b2) made up of unit matrixes and zero matrixes.

The present embodiment determines preferred puncturing patterns withfeatures of submatrix H′_(b2) and BP decoding taken into account.

BP decoding obtains a log likelihood ratio of each bit by repeating rowcalculations and column calculations.

The row calculation of BP decoding updates the log likelihood ratio. Inthis case, (puncture) bits that have not been transmitted are handled aserasure bits during decoding and since no initial log likelihood ratioexists for the erasure bits, the log likelihood ratio is set to 0. Whentwo or more erasure bits for which no initial log likelihood ratioexists are included in the same row, the log likelihood ratio is notupdated in the rows through the row calculation alone until the loglikelihood ratios of the erasure bits are updated through columncalculations. Therefore, the erasure bits in the same row are preferablyless than 2 bits.

A column calculation of BP decoding updates an extrinsic value. Theextrinsic value of an erasure bit is updated based on the additionresult of log likelihood ratios of “1” except for itself on the samecolumn. Therefore, when the column weight is large, the extrinsic valueof the erasure bit is updated based on the addition result of loglikelihood ratios of a plurality of 1's except for itself on the samecolumn, and therefore the absolute values of the log likelihood ratiosin the extrinsic value increase and this causes the log likelihoodratios to be more likely to converge. On the other hand, when the columnweight is small, the number of log likelihood ratios to be added issmall, and therefore the absolute values of the log likelihood ratios inthe extrinsic value are less likely to increase and this provides thenature that the log likelihood ratios are less likely to converge.

Especially when the column weight is 2, the extrinsic value is simplyreplaced for two 1's corresponding to column weight 2 in the paritycheck matrix, the absolute values of log likelihood ratios are lesslikely to increase, and reliability is not propagated even if iterativeprocessing is performed repeatedly, which may cause the receivingquality to degrade. Therefore, to appropriately update the magnitude ofthe extrinsic value, the column weight of the erasure bit is preferably3 or more.

Thus, when the feature of BP decoding is taken into account, from theperspective of row calculations, 1) the erasure bits in the same row arepreferably less than 2 bits and from the perspective of the columncalculation, 2) the column weight of the erasure bits is preferably 3 ormore.

The present embodiment will set puncturing patterns with 1) and 2) abovetaken into account. Hereinafter, a case will be described where a codedsequence is punctured using the number of columns of subblock matrix asa unit as an example.

When parity check matrix H_(b) of equation 9 is represented using thesubblock matrix as one unit, in submatrix H′_(b2), a relationship thatunit matrixes (“0”) are arranged in the i-th row and (i+1)-th row of thej-th column, zero matrixes (“−1”) are arranged in rows other than thei-th row and (i+1)-th row of the j-th column, unit matrixes (“0”) arearranged in the (i+1)-th row and (i+2)-th row of the (j+1)-th column,and zero matrixes (“−1”) are arranged in rows other than the (i+1)-throw and (i+2)-th row of the (j+1)-th column holds with j=q, q+1, q+2, .. . , q+s−1, q+s (where s is an integer equal to or greater than 1).

To be more specific, as is clear from FIG. 24, unit matrixes (“0”) arearranged in the first row and second row of the 22nd column, zeromatrixes (“−1”) are arranged in rows other than the first and secondrows of the 22nd column (third row and fourth row), unit matrixes (“0”)are arranged in the second and third rows of the 23rd column, zeromatrixes (“−1”) are arranged in rows other than the second and thirdrows of the 23rd column (first and fourth rows), unit matrixes (“0”) arearranged in the third and fourth rows of the 24th column and zeromatrixes (“−1”) are arranged in rows other than the third and fourthrows of the 24th column (first and second rows). Thus, as shown in thearea enclosed by a rectangular frame in submatrix H′_(b2) in FIG. 24,unit matrixes (“0”) are arranged neighboring each other in the same row.

In a unit matrix, only diagonal elements of the matrix are 1's and theother elements are 0's. Thus, if bits corresponding to columns of a unitmatrix are assumed to be bits not to transmit (puncture bits), there isonly one erasure bit in each row of the unit matrix. However, when unitmatrixes are arranged neighboring each other in the same row, if bitscorresponding to columns including the unit matrixes are assumed to bebits not to transmit (puncture bits), there are two erasure bits in eachrow.

To be more specific, when unit matrixes are arranged neighboring eachother in the same row as the unit matrixes (“0”) in the second row ofthe 22nd column and 23rd column in FIG. 24, if bits corresponding tocolumns including the two unit matrixes are assumed to be bits not totransmit (puncture bits), there is one erasure bit in each row of theunit matrix (“0”) in the second row of the 23rd column, there is oneerasure bit in each row in a view of each unit matrix, but since theseunit matrixes are arranged neighboring each other in the same row, thereare two erasure bits in a view of the same row in which unit matrixesare arranged.

As described in 1) above, erasure bits are preferably less than 2 bits.Therefore, to avoid 2 bit erasures, such a puncturing pattern will beused that bits corresponding to columns #21 and #23 in which no unitmatrixes are arranged neighboring each other in the same row are assumedto be bits not to transmit (puncture bits). That is, when bitscorresponding to column #21 are assumed to be bits not to transmit(puncture bits), bits corresponding to column #23 separated apart by thenumber of columns of 1 subblock matrix or more are assumed to be bitsnot to transmit (puncture bits). Thus, when the coded sequence ispunctured using the number of columns of the subblock matrix as a unit,by setting the puncturing interval to one unit or more (the number ofcolumns of 1 subblock matrix), bits erased by puncturing in submatrixH′_(b2) made up of unit matrixes or zero matrixes are only one bit ineach row and it is possible to avoid 2 bit erasures and thereby preventdegradation of receiving quality.

On the other hand, when such a puncturing pattern is used that bitscorresponding to columns #21 and #22 or columns #22 and #23 are assumedto be bits not to transmit (puncture bits), bits corresponding tocolumns of unit matrixes neighboring each other in the same row areassumed to be bits not to transmit (puncture bits), and 2 bit erasuresoccur and the reception characteristics deteriorate.

Moreover, when 2) above is taken into account, the column weight ofsubmatrix H′_(b1) of parity check matrix H_(b) is 3 or more, andtherefore by assuming bits corresponding to columns of submatrix H′_(b1)to be bits not to transmit (puncture bits), the log likelihood ratios ofthe extrinsic values are updated through column calculations so that theabsolute values thereof increases, the log likelihood ratios of erasurebits are more likely to converge and the reception characteristicsimprove.

FIG. 25 illustrates an example where bits corresponding to column #4 inaddition to columns #21 and #23 are assumed to be bits not to transmit(puncture bits). Since zero matrixes (“−1”) are arranged in the row of#23 in which unit matrixes (“0”) are arranged, if bits corresponding tocolumns #4, #21 and #23 are assumed to be bits not to transmit (puncturebits), the erasure bits of the row are kept to 1 bit in #4, and it isthereby possible to suppress degradation of receiving quality.

Puncture table (puncturing pattern) w when bits corresponding to columns#4, #21 and #23 are assumed to be bits not to transmit (puncture bits)is expressed as shown in equation 10.

[10]

$\begin{matrix}\lbrack 10\rbrack & \; \\{w = \left\lbrack {\underset{\underset{192}{︸}}{\begin{matrix}1 & 1 & \ldots & 1\end{matrix}}\underset{\underset{48}{︸}}{\begin{matrix}0 & 0 & \ldots & 0\end{matrix}}\underset{\underset{768}{︸}}{\begin{matrix}1 & 1 & \ldots & 1\end{matrix}}\underset{\underset{48}{︸}}{\begin{matrix}0 & 0 & \ldots & 0\end{matrix}}\underset{\underset{48}{︸}}{\begin{matrix}1 & 1 & \ldots & 1\end{matrix}}\underset{\underset{48}{︸}}{\begin{matrix}0 & 0 & \ldots & 0\end{matrix}}} \right\rbrack} & \left( {{Equation}\mspace{14mu} 10} \right)\end{matrix}$

0's included in puncture table w in equation 10 means bits not totransmit (puncture bits). That is, in the example shown in FIG. 25, bitscorresponding to columns #4, #21 and #23, that is, x192, x193, . . . ,x238, x239, p48, p49, . . . , p94, p95, p144, p145, . . . , p190, p191are punctured.

As described so far, when parity check matrix H_(b) is representedassuming a subblock matrix as one unit, the present embodiment assumesbits not to transmit (puncture bits) at an interval of one unit or more(the number of columns of subblock matrixes) when selecting bits not totransmit (puncture bits) using the number of columns of subblockmatrixes as a unit for submatrix H′_(b2) in which a relationship thatunit matrixes (“0”) are arranged in the i-th row and (i+1)-th row of thej-th column, zero matrixes (“−1”) are arranged in rows other than thei-th row and (i+1)-th row of the j-th column, unit matrixes (“0”) arearranged in the (i+1)-th row and (i+2)-th row of the (j+1)-th column andzero matrixes (“−1”) are arranged in rows other than the (i+1)-th rowand (i+2)-th row of the (j+1)-th column holds with j=q, q+1, q+2, . . ., q+s−1, q+s (where s is an integer equal to or greater than 1).

Furthermore, by assuming bits corresponding to columns whose columnweight is 3 or more as bits not to transmit (puncture bits) in submatrixH′_(b1) other than submatrix H′_(b2) above of parity check matrix H_(b),the log likelihood ratios of the extrinsic values in column calculationsare updated so that the absolute values thereof increase, and it isthereby possible to suppress degradation of receiving quality.

When bits corresponding to columns whose column weight is 3 or more areassumed to be bits not to transmit (puncture bits), if bitscorresponding to columns #21 and #23 are assumed to be bits not totransmit (puncture bits) in submatrix H′_(b2), bits corresponding tocolumns of zero matrixes such as #4 arranged in one row of unit matrixesincluded in #21 or #23 are assumed to be bits not to transmit (puncturebits). By this means, when bits corresponding to columns #4, #21 and #23are assumed to be bits not to transmit (puncture bits), it is possibleto suppress erasure bits of rows in which zero matrixes are arranged in#4 and thereby suppress degradation of receiving quality.

A preferred puncturing pattern for realizing coding rate 20/21 throughpuncturing from a QC-LDPC code having the parity check matrix ofequation 9 of coding rate 5/6 has been described. Furthermore, preferredpuncture table (puncturing pattern) w can be represented as, forexample, in equation 11-1 to equation 11-3 suitable for realizing codingrate 20/21 through puncturing from subblock matrix 216×216 having theparity check matrix in equation 9 of coding rate 5/6, that is, QC-LDPCcode of information size=4320 bits.

[11]

$\begin{matrix}\lbrack 11\rbrack & \; \\{w = {\quad\left\lbrack {\underset{\underset{216}{︸}}{0\mspace{20mu} 0\mspace{20mu}\ldots\mspace{20mu} 0}\mspace{20mu}\underset{\underset{4320}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{14mu} 1}\mspace{20mu}\underset{\underset{216}{︸}}{0\mspace{20mu} 0\mspace{14mu}\ldots\mspace{14mu} 0}\mspace{20mu}\underset{\underset{216}{︸}}{1\mspace{20mu} 1\mspace{14mu}\ldots\mspace{14mu} 1}\mspace{20mu}\underset{\underset{216}{︸}}{0\mspace{14mu} 0\mspace{14mu}\ldots\mspace{14mu} 0}} \right\rbrack}} & \left( {{Equation}\mspace{14mu} 11\text{-}1} \right) \\{w = \left\lbrack {\underset{\underset{432}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{20mu} 1}\mspace{20mu}\underset{\underset{216}{︸}}{0\mspace{20mu} 0\mspace{20mu}\ldots\mspace{20mu} 0}\mspace{20mu}\underset{\underset{3888}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{20mu} 1}\mspace{20mu}\underset{\underset{216}{︸}}{0\mspace{20mu} 0\mspace{14mu}\ldots\mspace{14mu} 0}\mspace{20mu}\underset{\underset{216}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{14mu} 1}\mspace{20mu}\underset{\underset{216}{︸}}{0\mspace{20mu} 0\mspace{20mu}\ldots\mspace{20mu} 0}} \right\rbrack} & \left( {{Equation}\mspace{14mu} 11\text{-}2} \right) \\{w = \left\lbrack {\underset{\underset{864}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{20mu} 1}\mspace{20mu}\underset{\underset{216}{︸}}{0\mspace{20mu} 0\mspace{20mu}\ldots\mspace{20mu} 0}\mspace{20mu}\underset{\underset{3456}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{20mu} 1}\mspace{20mu}\underset{\underset{216}{︸}}{0\mspace{20mu} 0\mspace{14mu}\ldots\mspace{14mu} 0}\mspace{20mu}\underset{\underset{216}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{14mu} 1}\mspace{20mu}\underset{\underset{216}{︸}}{0\mspace{20mu} 0\mspace{20mu}\ldots\mspace{20mu} 0}} \right\rbrack} & \left( {{Equation}\mspace{14mu} 11\text{-}3} \right)\end{matrix}$

A case has been described above where a coded sequence is puncturedusing the number of columns of subblock matrixes as a unit, but it mayalso be possible to set candidates for bits not to transmit (puncturebits) using the number of columns of subblock matrixes as a unit at aninterval of one unit or more (the number of columns of subblockmatrixes) and determine bits not to transmit (puncture bits) from thecandidates. In this case, suppose the candidates for bits not totransmit (puncture bits) are set using the number of columns of subblockmatrixes as a unit and are assumed to be bits corresponding to columnsnot including unit matrixes neighboring each other in the same row asdescribed above.

For example, as shown in FIG. 26, bits corresponding to columns #4, #21and #23 may be assumed to be candidates for bits not to transmit(puncture bits) and some bits encircled by broken line circles of x192,x193, . . . , x238, x239, p48, p49, . . . , p94, p95, p144, p145, . . ., p190, p191 corresponding to columns #4, #21 and #23 may be determinedas bits not to transmit (puncture bits).

Using this method, puncture table (puncturing pattern) w suitable forrealizing coding rate 16/18 through puncturing from a QC-LDPC codehaving the parity check matrix in equation 9 of coding rate 5/6 andsubblock matrix 48×48, that is, information size=960 bits is expressedas shown in equation 12.

[12]

$\begin{matrix}\lbrack 12\rbrack & \; \\{w = \left\lbrack {\underset{\underset{720}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{20mu} 1}\mspace{20mu}\underset{\underset{24}{︸}}{0\mspace{20mu} 0\mspace{20mu}\ldots\mspace{20mu} 0}\mspace{20mu}\underset{\underset{288}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{20mu} 1}\mspace{20mu}\underset{\underset{24}{︸}}{0\mspace{20mu} 0\mspace{14mu}\ldots\mspace{14mu} 0}\mspace{20mu}\underset{\underset{72}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{14mu} 1}\mspace{20mu}\underset{\underset{24}{︸}}{0\mspace{20mu} 0\mspace{20mu}\ldots\mspace{20mu} 0}} \right\rbrack} & \left( {{Equation}\mspace{14mu} 12} \right)\end{matrix}$

Furthermore, as another example, puncture table (puncturing pattern) wsuitable for realizing coding rate 16/18 through puncturing from aQC-LDPC code having the parity check matrix in equation 9 of coding rate5/6 and subblock matrix 216×216, that is, information size=4320 bits isrepresented as shown in equation 13.

[13]

$\begin{matrix}\lbrack 13\rbrack & \; \\{w = \left\lbrack {\underset{\underset{2808}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{20mu} 1}\mspace{20mu}\underset{\underset{108}{︸}}{0\mspace{20mu} 0\mspace{20mu}\ldots\mspace{20mu} 0}\mspace{20mu}\underset{\underset{1620}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{20mu} 1}\mspace{20mu}\underset{\underset{108}{︸}}{0\mspace{20mu} 0\mspace{14mu}\ldots\mspace{14mu} 0}\mspace{20mu}\underset{\underset{432}{︸}}{1\mspace{20mu} 1\mspace{20mu}\ldots\mspace{14mu} 1}\mspace{20mu}\underset{\underset{108}{︸}}{0\mspace{20mu} 0\mspace{20mu}\ldots\mspace{20mu} 0}} \right\rbrack} & \left( {{Equation}\mspace{14mu} 13} \right)\end{matrix}$

In these cases, it is also possible to prevent two erasure bits fromoccurring in each row, thereby obtain good receiving quality andflexibly set a coding rate after the puncturing.

Furthermore, although a case has been described above where codeword vof LDPC code is represented as v=[x0, x1, . . . , x958, x959, p0, p1, .. . , p190, p191], the order of the information sequence or paritysequence is not limited to this (e.g., the order may also be v=[p0, p1,. . . p190, p191, x0, x1, . . . , x958, x959] and the order ofinformation or parity is not uniquely determined), but bits not totransmit (parity bits) may be determined from the correspondence ofH_(b)v=0, in other words, the correspondence between the puncturingpattern corresponding to parity check matrix H_(b) and codeword v.

When, for example, bits corresponding to columns #4, #21 and #23 areassumed to be bits not to transmit (puncture bits), if codeword v isrepresented as v=[p144, p145, . . . , p190, p191, x0, x1, . . . , x958,x959, p0, p1, . . . , p46, p47], x144, x145, . . . , x190, x191, p0, p1,. . . , p46, p47, p96, p97, . . . , p142, p143 may be assumed to be bitsnot to transmit (puncture bits).

A case has been described in the above described example where arelationship that unit matrixes (“0”) are arranged in the i-th row and(i+1)-th row of the j-th column, zero matrixes (“−1”) are arranged inrows other than the i-th row and (i+1)-th row of the j-th column, unitmatrixes (“0”) are arranged in the (i+1)-th row and (i+2)-th row of the(j+1)-th column and zero matrixes (“−1”) are arranged in rows other thanthe (i+1)-th row and (i+2)-th row of the (j+1)-th column in submatrixH′_(b2) holds for j=q, q+1, q+2, . . . , q+s−1, q+s (where s is aninteger equal to or greater than 1), but it is also possible to obtain apreferred puncturing pattern using the above method of generating apuncturing pattern when cyclic shift matrixes of unit matrixes, insteadof unit matrixes, are arranged neighboring each other in the same row.However, when cyclic shift matrixes of unit matrixes are arrangedneighboring each other in the same row in submatrix H′_(b2), theconfiguration of the encoder may be complicated.

A preferred puncturing pattern may also be set for the QC-LDPC code ofcoding rate 1/2 in equation 8 using a similar method. A case with codingrate 1/2 will be described using FIG. 27.

As is the case with coding rate 5/6, for parity check matrix H_(b) ofthe QC-LDPC code of coding rate 1/2 in equation 8, puncturing pattern#p1 whose puncture cycle is the number of columns of submatrix H′_(b1)is used for submatrix H′_(b1) and puncturing pattern #p2 whose puncturecycle is the number of columns of submatrix H′_(b2) is used forsubmatrix H′_(b2).

FIG. 27 is parity check matrix H_(b) of the QC-LDPC code of coding rate1/2 in equation 8. Parity check matrix H_(b) in equation 8 is made up ofa subblock matrix of 12 rows and 24 columns. In FIG. 27, submatrixH′_(b2) is made up of unit matrixes and zero matrixes and submatrixH′_(b1) is outside submatrix H′_(b2).

In FIG. 27, #0 to #23 denote partial matrixes corresponding to therespective columns, submatrix H′_(b1) is made up of #0 to #12 andsubmatrix H′_(b2) is made up of #13 to #23. #13 to #23 are made up ofunit matrixes (“0”) and zero matrixes (“−1”). Thus, parity check matrixH_(b) of the QC-LDPC code shown in equation 8 includes submatrix H′_(b2)made up of unit matrixes and zero matrixes.

Hereinafter, a case will be described where a coded sequence ispunctured using the number of columns of a subblock matrix as a unit.

When parity check matrix H_(b) in equation 8 is represented using asubblock matrix as 1 unit, a relationship that unit matrixes (“0”) arearranged in the i-th row and (i+1)-th row of the j-th column, zeromatrixes (“−1”) are arranged in rows other than the i-th row and(i+1)-th row of the j-th column, unit matrixes (“0”) are arranged in the(i+1)-th row and (i+2)-th row of the (j+1)-th column and zero matrixes(“−1”) are arranged in rows other than the (i+1)-th row and (i+2)-th rowof the (j+1)-th column holds in submatrix H′_(b2) with j=q, q+1, q+2, .. . , q+s−1, q+s (where s is an integer equal to or greater than 1).

To be more specific, as is clear from FIG. 27, unit matrixes (“0”) arearranged in the first row and second row of the 14th column, zeromatrixes (“−1”) are arranged in rows other than the first row and secondrow (third to 12th rows) of the 14th column, unit matrixes (“0”) arearranged in the second row and third row of the 15th column, zeromatrixes (“−1”) are arranged in rows other than the second row and thirdrow of the 15th column (first row, forth to 12th rows), unit matrixes(“0”) are arranged in the 11th row and 12th row of the 24th column andzero matrixes (“−1”) are arranged in rows other than the 11th row and12th row of the 24th column (first to 10th rows). Thus, as shown in theareas enclosed by rectangular frames in submatrix H′_(b2) in FIG. 27,unit matrixes (“0”) are arranged neighboring each other in the same row.

In the case of coding rate 1/2, as is the case with coding rate 5/6,such a puncturing pattern is set that bits corresponding to columns inwhich unit matrixes are not arranged neighboring each other in the samerow are assumed to be bits not to transmit (puncture bits). When, forexample, a coded sequence is punctured using the number of columns of asubblock matrix as a unit and bits corresponding to column #20 areassumed to be bits not to transmit (puncture bits), bits correspondingto columns #15 and #23 separated apart by the number of columns of 1subblock matrix are assumed to be bits not to transmit (puncture bits).Thus, when a coded sequence is punctured using the number of columns ofa subblock matrix as a unit, the puncturing interval is set to one unitor more (the number of columns of a subblock matrix). Thus, in submatrixH′_(b2) made up of unit matrixes or zero matrixes, bits erased bypuncturing are only one bit for each row, and it is thereby possible toprevent 2-bit erasure and prevent degradation of receiving quality.

Furthermore, for example, bits corresponding to columns #15 and #20 maybe assumed to be bits not to transmit (puncture bits). #15 and #20 areseparated away from each other by one unit or more. Furthermore, bitscorresponding to columns #20 and #23 may also be assumed to be bits notto transmit (puncture bits). #20 and #23 are away from each other by oneunit or more.

All the bits corresponding to columns #15, #20 and #23 may not beassumed to be bits not to transmit (puncture bits), but bitscorresponding to columns #15, #20 and #23 may be assumed to becandidates of bits not to transmit (puncture bits) and bits not totransmit (puncture bits) may be determined from these candidatesaccording to the coding rate. By so doing, it is possible to suppresserasure bit in each row to one bit, obtain good receiving quality andflexibly set the coding rate after the puncturing.

Furthermore, of parity check matrix H_(b), since the column weight is 3or more in submatrix H′_(b1), by assuming bits corresponding to columnsof submatrix H′_(b1) to be bits not to transmit (puncture bits), themagnitude of an extrinsic value is adequately updated through a columncalculation, the log likelihood ratios of erasure bits are appropriatelyobtained and the reception characteristics are improved.

FIG. 27 illustrates an example where bits corresponding to column #10 insubmatrix H′_(b1) are assumed to be bits not to transmit (puncturebits). Zero matrixes (“−1”) are arranged in the rows of #10 in whichunit matrixes (“0”) are arranged in #15, #20 and #23, and therefore whenbits corresponding to columns #10, #15, #20 and #23 are assumed to bebits not to transmit (puncture bits), erasure bits in the rows are keptto one bit, which is more likely to suppress degradation of receivingquality.

Although a case has been described above where using the number ofcolumns of subblock matrixes as a unit, one subblock matrix is selectedfrom submatrix H′_(b1), a plurality of subblock matrixes are selectedfrom submatrix H′_(b2) and bits corresponding to columns of the selectedsubblock matrixes are assumed to be bits not to transmit (puncture bits)or candidates for bits not to transmit (puncture bits), the number ofsubblock matrixes selected from each submatrix is not limited to this,but a plurality of subblock matrixes may also be selected from submatrixH′_(b1).

The present invention is effective when a parity check matrix orgenerator matrix has regularity as with a QC-LDPC code.

The present invention is not limited to all the above describedembodiments, but may be implemented modified in various ways. Forexample, although a case has been mainly described in the abovedescribed embodiments where the present invention is implemented as anencoder, the present invention is not limited to this, but is alsoapplicable when the present invention is implemented as a power linecommunication apparatus.

Furthermore, this coding method can also be implemented as software. Forexample, a program for executing the above described coding method maybe stored in a ROM (Read Only Memory) beforehand and the program may beoperated by a CPU (Central Processor Unit).

Furthermore, the program for executing the coding method may be storedin a computer-readable storage medium, the program stored in the storagemedium may be recorded in a RAM (Random Access Memory) of the computerand the computer may be operated according to the program.

Furthermore, it goes without saying that the present invention is notlimited to radio communication, but is also useful for power linecommunication (PLC), visible light communication and opticalcommunication.

One aspect of the encoder of the present invention includes a codingsection that generates coded sequence s that satisfies equation 14-1,equation 14-2 and equation 14-3 for information bit sequence u and asetting section that sets a y-th puncturing pattern which corresponds tothe number of columns z from the (z×y+1)-th (y is an integer between 0and (n_(b)−1)) column to the z×(y+1)-th column and which has a cycle ofa divisor of the number of columns z, wherein of the coded sequence smade up of z×n_(b) bits from the first to z×n_(b)-th bits, bits to beremoved are determined from the (z×y+1)-th to z×(y+1)-th bits based onthe y-th puncturing pattern, the determined bits to be removed areremoved from the z×n_(b) bits making up the coded sequence s to form atransmission information bit sequence and the transmission informationbit sequence is outputted.

[14]GH ^(T)=0  (Equation 14-1)s ^(T) =GU ^(T)  (Equation 14-2)Hs=0  (Equation 14-3)where H is a parity check matrix of an LDPC code of (z×mb) rows and(z×nb) columns configured by arranging submatrixes of z rows and zcolumns in mb rows and nb columns, G is a generator matrix having arelationship of equation 14-1 with parity check matrix H of the LDPCcode and coded sequence s is a coded sequence made up of z×nb bits.

In one aspect of the encoder of the present invention, parity checkmatrix H of the LDPC code is defined by equation 15.

$\begin{matrix}{\mspace{85mu}\lbrack 15\rbrack} & \; \\{H = {\quad\begin{bmatrix}P_{0,0} & P_{0,1} & P_{0,2} & \ldots & P_{0,{n_{b} - 2}} & P_{0,{n_{b} - 1}} \\P_{1,0} & P_{1,1} & P_{1,2} & \ldots & P_{1,{n_{b} - 2}} & P_{1,{n_{b} - 1}} \\P_{2,0} & P_{2,1} & P_{2,2} & \ldots & P_{2,{n_{b} - 2}} & P_{2,{n_{b} - 1}} \\\vdots & \vdots & \vdots & \ldots & \vdots & \vdots \\P_{{m_{b} - 1},0} & P_{{m_{b} - 1},1} & P_{{m_{b} - 1},2} & \ldots & P_{{m_{b} - 1},{n_{b} - 2}} & P_{{m_{b} - 1},{n_{b} - 1}}\end{bmatrix}}} & \left( {{Equation}\mspace{14mu} 15} \right)\end{matrix}$where P_(i,j) is a cyclic permutation matrix of a unit matrix of z rowsand z columns or zero matrix of z rows and z columns.

In one aspect of the encoder of the present invention, the LDPC code isa QC-LDPC block code.

In one aspect of the encoder of the present invention, the LDPC code isa QC-LDPC code.

One aspect of the transmitting apparatus of the present inventionincludes a transmission section that is provided with the abovedescribed encoder and transmits the transmission information bitsequence.

One aspect of the coding method of the present invention includes a stepof generating coded sequence s that satisfies equation 16-1, equation16-2 and equation 16-3 for information bit sequence u and a step ofsetting a y-th puncturing pattern which corresponds to the number ofcolumns z from the (z×y+1)-th (y is an integer between 0 and (n_(b)−1))column to the z×(y+1)-th column and which has a cycle of a divisor ofthe number of columns z, wherein of the coded sequence s made up ofz×n_(b) bits from the first to z×n_(b)-th bits, bits to be removed aredetermined from the (z×y+1)-th to z×(y+1)-th bits based on the y-thpuncturing pattern, the determined bits to be removed are removed fromthe z×n_(b) bits making up the coded sequence s to form a transmissioninformation bit sequence and the transmission information bit sequenceis outputted.

[16]GH ^(T)=0  (Equation 16-1)s ^(T) =G ^(uT)  (Equation 16-2)Hs=0  (Equation 16-3)where H is a parity check matrix of an LDPC code of (z×m_(b)) rows and(z×n_(b)) columns configured by arranging submatrixes of z rows and zcolumns in m_(b) rows and n_(b) columns, G is a generator matrix havinga relationship of equation 16-1 with parity check matrix H of the LDPCcode and coded sequence s is a coded sequence made up of z×n_(b) bits.

In one aspect of the coding method of the present invention, paritycheck matrix H of the LDPC code is defined by equation 17.

$\begin{matrix}{\mspace{85mu}\lbrack 17\rbrack} & \; \\{H = \begin{bmatrix}P_{0,0} & P_{0,1} & P_{0,2} & \ldots & P_{0,{n_{b} - 2}} & P_{0,{n_{b} - 1}} \\P_{1,0} & P_{1,1} & P_{1,2} & \ldots & P_{1,{n_{b} - 2}} & P_{1,{n_{b} - 1}} \\P_{2,0} & P_{2,1} & P_{2,2} & \ldots & P_{2,{n_{b} - 2}} & P_{2,{n_{b} - 1}} \\\vdots & \vdots & \vdots & \ldots & \vdots & \vdots \\P_{{m_{b} - 1},0} & P_{{m_{b} - 1},1} & P_{{m_{b} - 1},2} & \ldots & P_{{m_{b} - 1},{n_{b} - 2}} & P_{{m_{b} - 1},{n_{b} - 1}}\end{bmatrix}} & \left( {{Equation}\mspace{14mu} 17} \right)\end{matrix}$

In one aspect of the coding method of the present invention, the LDPCcode is a QC-LDPC block code.

In one aspect of the coding method of the present invention, the LDPCcode is a QC-LDPC code.

One aspect of the transmission method of the present invention includesthe above described coding method and transmits the transmissioninformation bit sequence.

One aspect of the encoder of the present invention includes anarrangement section that generates information bit sequence u byinserting 0's in information bits and a coding section that generatescoded sequence s that satisfies equation 18-1, equation 18-2 andequation 18-3 for information bit sequence u, wherein, of the codedsequence s, bits always having “0” values are determined based onpositions in which the information bits are arranged and parity checkmatrix H of the LDPC code, the bits always having “0” values are removedfrom the coded sequence s to form a transmission information bitsequence and the transmission information bit sequence is outputted.

[18]GH ^(T)=0  (Equation 18-1)s ^(T) =Gu ^(T)  (Equation 18-2)Hs=0  (Equation 18-3)where H is a parity check matrix of an LDPC code of (z×m_(b)) rows and(z×n_(b)) columns configured by arranging submatrixes of z rows and zcolumns in m_(b) rows and n_(b) columns, G is a generator matrix havinga relationship of equation 18-1 with parity check matrix H of the LDPCcode and coded sequence s is a coded sequence made up of z×n_(b) bits.

One aspect of the transmitting apparatus of the present inventionincludes a transmission section that is provided with the abovedescribed encoder and transmits the transmission information bitsequence.

One aspect of the coding method of the present invention includes a stepof generating information bit sequence u by inserting 0's in informationbits and a step of generating a coded sequence s that satisfies equation19-1, equation 19-2 and equation 19-3 for the information bit sequenceu, wherein, of the coded sequence s, bits always having “0” values aredetermined based on positions in which the information bits are arrangedand parity check matrix H of the LDPC code, the bits always having “0”values are removed from the coded sequence s to form a transmissioninformation bit sequence and the transmission information bit sequenceis outputted.

[19]GH ^(T)=0  (Equation 19-1)s ^(T) =Gu ^(T)  (Equation 19-2)Hs=0  (Equation 19-3)where H is a parity check matrix of an LDPC code of (z×m_(b)) rows and(z×n_(b)) columns configured by arranging submatrixes of z rows and zcolumns in m_(b) rows and n_(b) columns, G is a generator matrix havinga relationship of equation 19-1 with parity check matrix H of the LDPCcode and coded sequence s is a coded sequence made up of z×n_(b) bits.

One aspect of the transmission method of the present invention includesthe above described coding method and transmits the transmissioninformation bit sequence.

The disclosures of Japanese Patent Application No. 2008-264382, filed onOct. 10, 2008, and Japanese Patent Application No. 2008-290022, filed onNov. 12, 2008, including the specifications, drawings and abstracts, areincorporated herein by reference in their entirety.

INDUSTRIAL APPLICABILITY

When, for example, a block code such as QC-LDPC code is used, thepresent invention can reduce the amount of transmission and suppressdeterioration of transmission efficiency while improving receivingquality and is useful as an encoder, transmitting apparatus and codingmethod for forming a coded sequence using a parity generator matrixpartially including zero matrixes such as a QC-LDPC.

REFERENCE SIGNS LIST

-   100, 100 a, 600 Encoder-   110, 110 a Zero matrix setting section-   120, 120 a Arrangement section-   130, 610 Coding section-   140, 630 Puncturing section (data reducing section)-   300 Decoder-   310 Fixed log likelihood ratio insertion section-   320 BP decoding section-   400, 500 Communication apparatus-   410 Coding section-   420 Interleaver-   430 Mapping section-   440 Transmitting section-   510 Receiving section-   520 Control information detection section-   530 log likelihood ratio calculation section-   540 Deinterleaver-   550 Decoding section-   620 Puncturing pattern setting section

The invention claimed is:
 1. An integrated circuit for a transmissionapparatus comprising: at least one input which, in operation, receivesan input; control circuitry, which is coupled to the at least one inputand which, in operation, controls: generating a codeword sequence shaving a first coding rate by performing a low density parity check(LDPC) encoding process on information bit sequence u to generate aparity bit sequence p, the codeword sequence s being made up of z×n_(b)bits, the information bit sequence u being made up of z×(n_(b)-m_(b))bits, the parity bit sequence p being made up of z×m_(b) bits, z beingan integer equal to or greater than 1, n_(b) being an integer equal toor greater than 1, m_(b) being an integer equal to or greater than 1,the codeword sequence s being a sequence having the parity bit sequencep concatenated at a latter part of the information bit sequence u, thecodeword sequence s being decoded at a decoder of a communicatingpartner apparatus; forming a codeword sequence sp having a second codingrate by removing one or more sets of consecutive y bits from the paritybit sequence p, by using a removing pattern indicating whether or noteach set of bits from a first bit to a z×m_(b)-th bit of the parity bitsequence p are removed, y being a divisor of z; modulating the codewordsequence sp having the second coding rate to generate a modulated symbolsequence; and transmitting a transmission frame including the modulatedsymbol sequence.
 2. The integrated circuit according to claim 1, whereinthe codeword sequence s satisfies Equation 1,Hs=0  (Equation 1) where a parity check matrix H has z×m_(b) rows andz×n_(b) columns configured by arranging submatrixes of z rows and zcolumns in m_(b) rows and n_(b) columns.
 3. The integrated circuitaccording to claim 2, wherein the parity check matrix H of the LDPC codeis defined by Equation 2: $\begin{matrix}{H = \begin{bmatrix}P_{0,0} & P_{0,1} & P_{0,2} & \ldots & P_{0,{n_{b} - 2}} & P_{0,{n_{b} - 1}} \\P_{1,0} & P_{1,1} & P_{1,2} & \ldots & P_{1,{n_{b} - 2}} & P_{1,{n_{b} - 1}} \\P_{2,0} & P_{2,1} & P_{2,2} & \ldots & P_{2,{n_{b} - 2}} & P_{2,{n_{b} - 1}} \\\vdots & \vdots & \vdots & \ldots & \vdots & \vdots \\P_{{m_{b} - 1},0} & P_{{m_{b} - 1},1} & P_{{m_{b} - 1},2} & \ldots & P_{{m_{b} - 1},{n_{b} - 2}} & P_{{m_{b} - 1},{n_{b} - 1}}\end{bmatrix}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$ where P_(i,j) is a cyclic permutation matrix of a unitmatrix of z rows and z columns or zero matrix of z rows and z columns.4. The integrated circuit according to claim 3, wherein the LDPC code isa quasi-cyclic low density parity check (QC-LDPC) code.